There is not really much you could do. There is lots of room on BS though, so there would have to be more than 6 people to be filling. There is another ok ledge that I remember but it is like 8 pitches below BS, so really that is not a good option. You'll know when you start up if a jam at BS is a possibility. If so, try another day or be prepared to get cozy.
If you can make Big Sandy with bivy gear, you can probably make the summit in the same amount of time with no bivy gear. I would guestimate that maybe 1-2 / 10 ascents haul these days, and probably half of those bail - all are gumbies. Big Sandy is pretty big. If it's crowded, your day of climbing probably sucked - waiting behind all those people. Bring an extra day of food and be first in line the following day after just chilling at the base - whether doing it IAD or with a bivy.
Climb the first two pitches of the zig-zags and bivy in the hole. Then toss yer crap down on those on Big Sandy who would not make room for ya. And when you wake up in the morning you will be in front of everyone. Which will a good thing cause if there are that many parties on Big Sandy you sure as hell do not want to be behind the shit show that is going to happen in the morning cause being the last party to the ledge means you're going to be the last to leave. And you could be there for a really, really long time.
Don't throw your crap anywhere. Carry a way to take a crap and carry it out. There is no reason IAD or bivying parties should be doing anything else. Shit chimney needs to earn a new name.
Big Sandy is an amazing bivy. Doing the route in a day is fun too, just different. Arrive at the base mid day, fix to the top of 3. Establish that you will be the first in line wall style party, and that you will be heading up early. Allow fast teams to pass before the bolt ladder, and only if they really are faster than you. Keep your haulbag light! (like wear on your back through the 5.easy bit below the bolt ladder). D