I'd like create a class/struct/other that contains each measure of a song, complete with independent tempo and beat count, then play the entire song back (with potential updates from user input). I'm only aware of how to change those variables on an AKSequencer track as a whole; is there a way to store that data independently and then have it play back as one? And keep coherence between the measures so as not to "jump" between them? Thanks!
AKSequencer is not good at setting loop length on the fly, but it is totally fine for adding to or re-writing the contents of a track while the sequencer is running. This includes tempo events.
Why don't you set the length to something arbitrarily long, and string together your MIDI events measure after measure without ever looping? Keep track of how many beats have been written so far, and just keep adding after that point. Doing this while the sequencer is running should be no problem. You could even automate writing the next bar by triggering a callback function near the end of each measure getting it to write the next segment (which could be selected or 'cued up' at run-time). You can schedule the tempo events with addTempoEventAt(), with the starting point for the next segment.
When your user stops the sequence, clear the track(s), reset the tempo, rewind the sequence and start over.