Well, the issue seems to be resolved now. That said, I don't know what the issue was, but I can zap again today.
I didn't initially have the same string on both accounts. It just stopped working for this account a few days ago.
Initially, I thought it might just be a temporary thing with the mint, but it didn't resolve after 3 days. So I uninstalled Minibits, restored my wallet, made a new connection string, and the issue persisted.
But, it worked when I put that string on another Amethyst account as a test.
So, I have no idea why things were broken for me, but they seem to be working now.
Thank you for your assistance (and amazing product)!