best software for multicam video production
Premiere is your best option unless you plan on spending a boatload (thousands and thousands) on an Avid system.  I'd suggest working on smaller sets of cameras at a time and then working off the combined feeds.  You can use multicamera editing mode with several cameras at a time, make the best choices out of those and then run each of those sequences in to another multicamera sequence to further resolve them.

The process is going to kind of suck no matter what system you do it on because it is a boatload of synchronous footage to go through.