I have a similar problem, if not for similar reasons. The software that I utilize to solve it is The Keep, by NBOS.

It's a bit pricey, which made me take while to get it, and it does have a certain idea in mind of how it wants you to keep track of information- but if you can adapt, it works well.

First, from their blurb:

Key Features:

• Organize your campaign information into intuitive folders
• Track notes, maps, images, character sheets, handouts, and PDFs
• Easy to use, tabbed based interface
• Integrated word processor with spell checker
• Fractal Mapper integration
• Built-in Dice Roller
• Inspiration Pad Pro integration for random names and encounters
• Revision Tracking and Automatic Backups
• Print a single document from your notes, maps, images, and character sheets
• Create eBooks from your database
• Game-system independent
• Expandable using HTML based plugins
• Can be run from Dropbox and Google Drive folders, or from USB Flash drives and other removable drives

For my review of it- I'll start with the pros:

• System Agnostic- I use it for a few campaigns for different systems, and it works the same no matter what.
• Fractal Mapper integration- I actually like Campaign Cartographer more, but the integration is just great for getting maps into the system, so much that I've begun using FM more.
• Tab based, tree based paradigm- very easy to get accustomed to.
• You can use it locally, or store it on Dropbox for use in the cloud.
• It has a fully integrated word processor with a customizable spell checker.
• It has integrated PDF viewing
• You can make handouts for exporting and giving to players.
• It integrates with their character sheet designer/viewer
• It includes revision tracking
• It can export the information in a variety of formats, and (at least so far) isn't so unwieldy that I can't do it as needed.
• You don't have to export everything when exporting.
• Very good developer and community support.

Cons:

• The interface is a bit... archaic. Personal choice as an interface designer...
• It has a word processor with its own format. I prefer plain text with Markdown, so it was hard getting used to using a word processor again.
• If you already have a lot of data, there's no easy way to import it other than copy and paste separately.

I think it comes close enough to your needs that you're likely to find it useful- and it's definitely built from an RPG perspective.

One last note - you don't have to buy it from NBOS.. you can get it from Drive-Thru RPG, and sometimes they have it on sale. There's currently a bundle with it and Fractal Mapper that's less than the two separately.

UPDATE: After posting this, I was corrected- the Keep does allow you to do hyperlinking. I'm not sure when this was added, or if I've just always overlooked it.

Playing short form requires several shifts in technique and approach. My group typically does 2-3 hour sessions. A 4 hour session is a marathon for us.

Drop the Filler

The first thing to do is let go of filler material. Filler material includes setting up adventures that are "clue to clue to clue to oh actually interesting development". This is the default for a lot of play, and it wastes time. Let go of having the players play out haggling for everything, or explain each store they go to for supplies, and so on.

If there are encounters that would take up time but not actually provide interesting choices or hard implications? Cut them out.

There's also a lot of time wasting in putting in situations that make it unclear what the players should even be trying to do. "Where should we go next?" "I guess we keep searching until we find a clue of what to do next?" etc. Videogames used to use mazes to add extra hours of gameplay as a filler device, and this is the same kind of thing.

Let players get to the fun interesting stuff without this obfuscation and play not only goes quicker, it's more fun period.

Scene Framing

Scene framing is the next step. You no longer say, "Ok, where do you want to go next?" as the default question. If you know the general thing the players are doing, you skip up to the next part and get right into it.

For example, you know the players are trying to track down a cult:

"After three days of talking with shady people, listening to wacked out babbling of street preachers, and having to do some small trading in hallucinagens, you finally find out where they're having meetings. At dusk, you find yourselves outside an abandoned church where several people died of plague years ago..."

Think of how movies or tv shows will give you a montage - so you can skip the legwork and go RIGHT to the interesting stuff. This alone cuts out a LOT of time wasting material.

The Rules you use matter

If you're playing a game where combats take 45 minutes... well, one combat will take up a significant chunk of your time. Understand that many of the older games and traditional games expect you to be playing for 6-8 hours as session, so if they expect 5 combats in a session, and you've got 3 hours to play... it's not going to fit.

If you're playing a game where conflicts of all types, take 5 minutes? Well, then things move much quicker. So pay attention to what rules you're using and what their impact is, so you can plan appropriately.

Getting into character, exploring the world, etc.

I've been playing this way for several years now. My group gets into characters quite well, because the focus of our play is on characters, their issues and personalities, which is because a lot of our game time is putting the characters into crisis points and fun interactions.

I find a lot of people used to playing with lots of time, think the solution to character or world development is simply pouring on more time, when in fact, it's about directed and focused play. I've had several people say, "We've done more in this two hour one shot than I've done in entire campaigns, for years."

That's because I cut out the filler, focus on the characters' choices and actions, and try to give situations that are at turning points. Each scene should matter and have some impact.