I'm currently struggling with this because I'm getting into Glorantha, which is one of the Big Three settings (Tékumel and Hârn are the other two). The Big Three dwarf even settings typically considered huge, like the Forgotten Realms, and it's daunting to try to figure out how to eat this aircraft carrier, let alone how to prepare some of its most choice bits for my players.

Two things have helped me immensely:

1. My setting will vary.

   This isn't a choice I'm making, it's an inevitable fact that the Glorantha community hammers into newcomers, and it's true of all campaign settings. It's impossible to create and play adventures in a setting that are 100% true to existing canon, because there are always details that you have to make up and those will be different than what the creators would have put there. They might even contradict your decisions with a future book! At some point during play, you will say something that contradicts canon, and that's OK. It's true for this game, and the play's the thing!

   This is true of all settings that see actual play. And you want to see actual play with this setting, right? That means you have to hold your nose and jump into the messiness of actually using the material, knowing that you're going to "break" things by playing with them. That's okay though: a toy left in it's pristine packaging isn't a toy, it's a collector's item. If you just want to read and enjoy the setting as a written artifact, you can totally do that and that's a valid consumer choice! But if you want to play with it, you have to let your toys get marker on them and sandbox sand in their joints. Toys that are played with inevitably change from how they were originally crafted. It's the nature of play.

   (Fortunately, when it comes to settings you can have your cake and eat it too: you can appreciate the setting as a literary creation as well as play with it, so you can keep a collector's item and have a toy copy to play with. Scratches your toys get won't change the literary canon, and your appreciation of the canon will inform your play organically as you exert your creative muscles during play.)

2. You don't have to eat the whole cow.

   A big, complex campaign setting isn't something to consume in its entirety before regurgitating it to your players. It is raw material to use in your actual table-time gameplay. If a bit of material is not getting used, it is fundamentally useless. If that bit of material is actively preventing play, it is worse than useless. You have to—for the moment—abandon the urge for authenticity that your love of the setting inspires in you, and instead go for pragmatic utility.

   Instead of trying to portray the setting to your players as a perfect, untouchable jewel (see how unplayable that sounds?), treat it as a massive treasure pile to mercilessly pillage for bits and pieces as you need them.

That's the theory and mental gymnastics to get back into a useful frame of mind. But how about practical advice?

Zoom in. Break it down.

No game will ever use all material from a big setting. Pick a spot that interests you, and ask yourself "What is here?"

You can answer that question however you like, drawing on stuff you've already digested about the setting and your own novel creations. You don't have to respect the canon over your own creations either, since this isn't about Perfect Jewel Setting Appreciation (PJSA), it's about getting the toys out of their packaging and into the backyard to produce Fun™.

Your answers will prompt more questions. Answer them in the same way. Build out your own imagination as you prepare your notes for playing in this area. Not only will you achieve freedom from the PJSA paralysis, but you'll also have the details relevant to playing here closer to your fingertips than if you were relying on the pre-written canon as your reference.

There was a great thread on Story Games about exactly this process: how to zoom in on a big, complex setting and create something that's table-level gameable: Giant Detailed Settings And Story-Gaming! (Don't worry about the "story-gaming" in the title. It turned out to actually be about the GM prep that's universal to GM'd RPGs.) I discovered the thread earlier this month and reading it has massively de-escalated my GM paralysis around how to play in Glorantha.

The executive summary of the article is:

0. Pick a setting, any setting. You don't even need to know anything about it for this to work—knowing stuff is bonus.

1. Pick a place in it. You can pick by opening the book to a random page or by choosing it, it doesn't matter, the method works regardless.

2. Read the introductory blurb about the place.

3. Reading nothing more, chop that up into four factions. You might be making stuff up about something mentioned merely in passing at this point to get four, but that's OK. The point of this is that you're thinking local now, instead of global. The paralysis is abating already...

4. Take two of these factions and ask how they could be in conflict over or via a third. Leave the fourth in reserve. This is your campaign premise.

   (This might sounds like you're about to embark on a scripted campaign, but it doesn't—if you're wanting to run a sandbox, you need situation and moving parts as context, and this gives you that. But yeah, if you're going to make a plotted campaign, this gives you your plot frame. It's flexible.)

5. Now expand your idea by going and mining the setting for related details. Again, the big setting will provide raw material, but you'll be crafting with them: bending, cutting, folding them and providing the glue ideas.

6. You now have a situation that's big enough to generate dozens or more of sessions of play, and local enough to be actually playable. And you're really familiar with it!

7. This step is whatever your usual campaign-preparation and first-adventure-writing process is, now that you've broken past the GM paralysis of the big setting.

8. Go play!

The point of the summary is more to show how simple it can be to use a Big Damn Setting for actual play. The actual thread is well worth reading in its entirety for the discussion of the method and related issues. But for convenience, here are direct links to the [four] posts the method and some of its commentary is spread across (these don't correspond to the number above, that was just my own breakdown of the process): 1, 2, 3, 4, 5, 6, 7, 8.

But what about incorporating material later?

You're creative, you'll figure out how to incorporate material that you're excited by into your ongoing campaign when you come to actually doing it.

This is one of those things that is only worrying when you're not actually facing it, and is obvious how to tackle when you get to it. For now, remember only this: the material is incomplete before it hits actual play, and needs your creative decisions about how to use it, in order to be gameable. Big settings are saying, "You complete me!"

Relapse will happen

You will keep struggling with the desire to preserve and represent to your players the perfect jewel that is the canon. You can't help it, you love the setting. But as often as you need to remind yourself of it (and I need it a lot): remind yourself that your actual-play setting must and will be different than your canon-appreciation setting, by the very nature of having the privilege of playing in it.

Just think of all those GMs out there who are actively running this setting: they're out there breaking it! They're getting marker on their Barbie dolls and sand in their vintage Transformers, because that's what play requires. Be envious of the GMs who get to actually play in this setting. Make a personal talisman of this envy. Work that envy up real high so that it will motivate you, too, to break the setting out of its bubble package so that you can join them.

Most of 4e’s published (hardcopy) material was not Forgotten Realms and I don't think there are any specific 4e accessories for Amn. Fortunately for you, most of the 4e Living Forgotten Realms adventures are available for free online. While I don't know if there are any additional adventures based in Amn itself, as you noted there are a couple of Amnite colonies—Port Nyranzaru in Chult and Snowdown in the Moonshae Isles. Available Living Forgotten Realms adventures in the Moonshaes involving Amn and Amnian mercenaries are:

• Nature’s Wrath – Amnite pirates in the Moonshaes
• Black Gold – An Amnite agent in the Moonshaes
• Black Blood – A major encounter with Amnian mercenaries in the Moonshaes
• Black Heart – Adventure ties in with the Amnite agent from Black Gold

For more in-game historical background, there are the Forgotten Realms Campaign Setting and Player’s Guide for 3e, particularly the Shadow Thief of Amn Prestige Class in the latter.

In addition, AD&D 2e contains several Forgotten Realms accessories that directly deal with Amn, although these take place during the Time of Troubles in Faerûn before the Spellplague of 4e. Specifically,

• Lands of Intrigue – Book Two: Amn (60+ pages)
• Empires of the Sands – The first 18 pages are dedicated to Amn
• Volo’s Guide to the North – Many references to Amn are interspersed throughout

You could also use material from Baldur’s Gate 2: Shadows of Amn, the computer game and the novel, which are centered in Amn and prominently feature Spellhold.

Dragon and Dungeon magazines have some Amn-related articles. For example, "Crimmor: City of Caravans" by Ed "I am Elminster!" Greenwood in Dragon #334 (pp. 22-34) is a loquacious, detailed treatment of the "Crossroads of Amn," including a keyed map, that was nominally for 3.5e but contains almost no mechanical information. (Courtesy of @HeyICanChan. Thanks!)

There are a couple of old 4e WotC forum threads on Amn. One, entitled "Heroic Tier Adventure Ideas for Amn," is self-explanatory and the other is "Meldread's Amn," one DM's detailed version of Amn about 100 years after the Spellplague, including maps.