A. Crowding the battlefield with a couple dozen enemies
B. Sending them up against something that only some of them can hurt?
Thanks for your help and any further insight into DMing larger groups would be a great help!
Well, the nice thing about using multiple enemies is that it limits the chances that some people can't affect the one thing they're fighting. If they can't hurt monster X, they can move onto monster Y. Also, you'll want to avoid using single monsters due to action economy. With a group that big, the players will be getting six actions to its one. One of two things will happen: they'll murder it, or if it's strong enough to survive, it will likely murder them.
Also, just for sake of sanity, avoid or seriously limit a few things:
- PCs that summon more miniatures on the board (looks like the group won't be doing that, anyway).
- Splitting the group up.
If PCs are summoning too much, it will really slow combat down. Splitting up is sometimes unavoidable. This is where Sirpercival's suggestion of a Co-DM comes in really handy (I've never run a big enough group to try this, personally).
Also, make sure you're up on any special rules that might come up in a particular adventure (if you know they're going under water, make sure you know how Swim and drowning work) to save time of you looking up rules. Try to encourage the players to think about their next action on other player's turns. With six people a round thinking about and giving actions, all that decision time can really add up!
Good luck!