The system is designed to accomodate this

...but without the DMG it's a little tricky.

The science:

Basically, each enemy has an XP value. This is how much XP it's worth when it's defeated (divided among those who defeat it), but it's also useful for building encounters.

Here's how you build an encounter in 4e: You take the XP value of a "standard"-type enemy of the same level as the party, and multiply that number by the number of PCs in the party. The result gives you a "budget" that you use to "buy" enemies to create an encounter of average difficulty (the party is unlikely to die, but will expend a noticeable amount of resources --consumables, healing surges, daily powers-- during the fight).

For a more difficult fight, increase the level of the standard-type enemy whose XP you're using as the baseline multiplier to get your budget, up to four or five levels above the party. For an easier fight, drop the level down by three or four. The extreme ends of this will produce boss-level fights, or make-the-players-feel-invincible routs.

The art:

The DMG recommends actually using enemies up to five levels higher than the party for boss fights, but in my experience this is more frustrating than interesting; it's better to use "solo" type monsters of the party's level. The challenge level will be similar but more fun.

Combine standards, elites, and minions for interesting fights. Minions die quicker and elites last longer, so if there's an NPC or ability you want to be present throughout the fight make it a tougher monster type.

Use soldier (defender) and lurker types for longer more drawn-out battles, brutes and strikers for shorter, more intense fights.

If you've got a combination of enemies whose abilities support each other in significant ways, or you're adding strange terrain, remember that this may make the fight harder than its XP budget will imply.

The mechanics of monsters changed partway through 4e's tenure

With the publication of the Monster Manual 3, monsters got their hp reduced, their damage increased, and their powers were made a bit more interesting. This makes fights take a little less time while being a little more tense, but the overall resource drain per fight is pretty much the same. If you can get your hands on them, use post-MM3 monsters whenever possible until you're familiar enough with them to adjust the earlier monsters to fit that ethos. If you can't, don't worry about it too much. You'll learn to fiddle with monsters based on experience, and until then the fights will be a little more tedious than they'd be with MM3 monsters.

To that end, seriously consider a D&D Insider subscription. It provides a searchable compendium of every mechanic --rule, monster, item, class, race, etc-- ever officially published, a solid character builder AND a solid monster builder, and downloadable access to all the Dungeon and Dragon magazines for 4e. AND all the errata are kept up-to-date across the compendium and builders. I was suspicious of the service at first, but quickly found it to be nearly indispensable.

I would recommend doing the following changes.

1. Expect the characters to reach level 12.
2. Give the characters very powerful magic items.
3. Reduce the CR 17 big bad to a CR 15 big bad. If the big bad needs to be level 17 to have access to a spell, ability, or collection of spells, then give the big bad an item which replicates that spell. (For example, perhaps the power comes from the building they occupy, combined with some artefact, rather than their own skill) Alternatively, you can reduce the CR by giving damage vulnerability, or fewer HP.

This should allow them to level up over 2 or 3 sessions, and give enough fights between levels to feel the achievement. The extra magic items will allow the big bad to be a challenge but beatable and you won't have to adjust your planned content too much. My advice is partially based on the fact that the published adventure themselves don't actually take characters to level 20.