How do I begin to troubleshoot aCal?
I'm having similar issues on a Kindle Fire with iCloud. One quirky workaround is to open Settings | Servers and disable your server(s). Then re-enable them. That seems to force an update.

Edit:
a) Not sure about all calendars.b) Right, it's a workaround, not a fix. But it address your questions:

"I can't figure out how much of this is aCal,"
Likely most of it, aCal being the one common element in both our observations.

"*how much is my phone, *"Less likely, for the same reason.

"*and how much is bad data from my CalDAV server (Chandler Hub) *"Ditto.