With 3 players, you aren't lacking too hard on the action economy. Especially if your players have animal companions, or you are agreeable to the Leadership feat.
If the players aren't keen on playing secondary characters (even if they are simple in tactics), then here's where Gestalt would really come into play.
Make sure they choose options that keep their ability sets varied. No need for 3 Fighter/Rogues, for instance...
Alternatively, you can do what I did recently and give a "partial" gestalt. My players didn't like the idea of being "super humans" vs normals, so I only gave them about a class feature or two to make up for the lack of versatility.
Better BAB and combat access for the Rogue (since there was less flanking options). Increased spellcasting and allowing arcane spell choices for the Ranger. That kind of thing.
It helped that one player was keen on playing a Leadership style character (to gain a dedicated healing cohort... called Jeeves... who they dress up in a butler's outfit... /sigh). The player wanted me to play the character, so I got a DMPC that fills a needed role, and they got a powerful feat option (I play him as that player's bodyguard, protecting him first, party second, etc).
Basically, however you can try and fill that "4th role" that's going to be missing. Whether it's adding characters (under DM or PC control), adding items, adding class abilities, or whatever.
Obviously if you are going to run a homebrew, then ultimately you control the encounters (or you can let the PCs play a game where they control the encounters, and decide who and how to face their enemies, etc), so all that might end up being unnecessary.
You did say you were planning on using APs to cut on prep time though, so it's likely you'll need to decide on some option for the players.
