Final (hopefully) update: more than 96 hours after the cancellation, still no miles my the account. Called AA once again, and from the first few moments I felt I won the agent lottery and got a competent and helpful one, which proved to be true.

He mentioned that the there was a refund request (of miles & taxes) still in process and he didn't give any bull timeframe of "1-2 days" etc. He called the help desk and came with no news. Then he said he could still ticket the new reservation that I had on hold, with a note of some sort that it would use the miles from the cancelled reservation. I said "Yes please" and he proceeded to take my credit card info etc. So nice and painless. I checked the AA website and the status on the new reservation indeed changed from "On Hold" to "On Request". I think that's what the original agent I spoke to was supposed to do in the first place, but she was too incompetent to do that.

So the take away for the future is: if you have to redeposit miles to make a change in an award reservation (like I had to do), the agent should be able to request ticketing for the new reservation immediately. If the agent says you have to wait a few days for the old miles to redeposit, they probably don't know enough and you should try a different agent.