I'll be damned, it worked. I left it in the bag for weeks, pulled it out, and tried it in different modes — no beeping. Put all the covers back together and put it back in the bag again. Tried the DMM again today — still no beeping.
Winter humidity in my office was the issue, at least for me.
I think it might be useful to have an option to turn lead detection ON/OFF in a future firmware update. That way, if someone doesn't have time to dry it out right away, they can still use it.