Heh, I'm a firm believer that almost nothing is impossible.
If the briskets will fit in a 20-25l enclosure, then you're well within the realm of what the APC was designed to do. If you're using a considerably larger container (such as a really big camping cooler), filling it with hot water will lessen the load on the APC to get the container to temperature.
Two things I would do to make it easier on the APC with your briskets:
1) Let them thaw in the fridge for a day before your cook (if they're frozen)
2) Let the bath come up to temperature before putting the briskets in.
In terms of impact - 15lbs vs a large (48qt ice chest as acs suggested) isn't that significant, provided they're at least not frozen.
In terms of how you place the briskets in the bath - ideally, you want something like a cooling grid on the bottom of the vessel to hold them up off of the bottom - you want the water touching all sides of your meat, so you get even cooking throughout.
People use clips to keep their bags from floating. If you do a good job of getting the air out before you put them in the bath, and they're fairly large pieces of meat, they may not end up floating at all.
If you use (ideally freezer) ziploc bags, you can always pull them out briefly and re-displace out the air if it becomes too much. For the most part, I haven't found floating to be a problem with meat.
The reason that you finish in the oven is to get that nice sear on the outside of your brisket.
Don't be afraid of it...sous vide cooking is very forgiving!!! I think you'll do fine!!