Agree with the majority sentiment that splitting teams to play over multiple days goes against what most people feel this even should be about, so definitely wouldn"t want to see that.
If sufficient capacity cannot be found to host all/most of the teams who want to enter, what about teams having to qualify online in some way? I know this means that some teams would still be excluded from the live event (as they are now), but at least every single team which wanted to enter would have a shot. How you wanted to structure this could vary, either straight satellites yielding the required number of team spots, or some format (league or otherwise) whereby stacks can be carried through, or even redistributed amongst team members to some limited extent (maybe averaged?), you get the idea.
Alternatively, rather than splitting teams across two Day 1"s, what about splitting the field, but keeping teams together? I know this could obviously create some "unfairness" if many of the perceived tougher teams are in one day, but if it"s a random draw, then it is what it is... Would allow capacity to be significantly increased and also keep all team members playing in the same Day 1...
Just my thoughts anyway, whatever happens I know I"d personally be gutted if I wasn"t able to compete in this event, outside of the Worlds, it"s the one APAT I would never want to miss, so I understand wanting to give as many people the opportunity as possible.