Well, I've learned my lesson. Always up the gas fees to the "fast" recommendation, because if a transaction gets 'stuck' there's no way to move forward with a new transaction until that one either succeeds, fails, or is cancelled, and you have to pay gas to cancel it (and if the gas you pay to cancel is too low, the cancel can literally take days).

So, just bite the bullet and pay the premium to make sure your transactions don't get stuck in Ethereum hell. (Also, if you're using UniSwap, if the transaction takes longer than the timeout interval, which is 20 minutes by default, then you still end up paying the ETH gas fees, but the transaction gets rejected by UniSwap -- so it's gas paid literally for nothing).