Combat takes forever even if I have one player help me and allow them to go 2 at a time.
I applaud you for tackling this from a traditional D&D approach. That said, I recommend a war game. Pull ideas in from the 3.5 Heroes of Battle or any other mass combat game. Specifically:
- For ranged attacks like fireballs or artillery that could affect
the whole party, roll damage dice ahead of time and note it.
- Flesh out types of enemies instead of specific enemies. Ie. "goblin,"
"goblin guard" (3rd level warrior?), "goblin prince" (6th level
fighter?). Then not only is prep simpler but you'll be juggling less
varied creatures in combat.
- Green screen! For overwhelming numbers, use the 'scrubs' concept from GURPS (where I first encountered it, at least). Some enemies are just pawns to be tossed aside, so a single hit will suffice. Added bonus, used sparingly this can make the fighter/paladin/barbarian feel like they're just that cool. Just up the amount of minions used, in a 4e game.
- Consider having multiple choke points for PCs and enemies alike. Then you could maintain you multiple-turns-simultaneously approach and give it an in-game reason.
When we do story based adventure there are 2-3 players that do most of the talking and the others twiddle their thumbs.
Grant each (or even subgroups) of PCs separate 'orders' or intentions. For example, in any given roleplay this group of sorcerors could be looking to replenish the parties consumable items and the paladin and cleric could be gathering intelligence about what undead are about. If everyone has their own distinct goal, or at least multiple shared goals, everyone can get more of the spotlight since they'll have different concerns.
Expanding on the above, focus each encounter on **whoever spoke least in the last one. The paladin didn't get to talk with the guildmage much? Well, the wizard might not have much to say to the archdeacon of the paladin's church - at least not as much as the paladin would. In this way you can bring even shy/passive players to the front of the party. While my group has been big but not as big as yours, I've tried this and it works.
I've tried encounters with many foes, encounters with only a few tough foes, dialog only encounters, social puzzle encounters, everything I can think of. What else can I try to get this group more engaged?
If I were to go with such a large group, I'd definitely try out a Dirty Dozen war campaign at least once. Some of HoB is RAW 3.5 mechanics, but even that might be easy to translate to your 4e game. A lot of it is simply DM tactics to use with the group, from planning encounters to designing a battlefield to handling large scale battles.
Note it doesn't take into account large parties (anywhere I know of) but with a bit of tweaking, tactics to handle large parties on the NPC end can be applied elsewhere. Maybe your wizard could roll their spell damage when they prepare their spells, even?