I've often heard submit/don't submit to more than one publication.
Many (but not all) genre publications say they don't allow simsubs. But authors withdraw all the time, for example, if they decide they want to submit the story somewhere else, instead. It's part and parcel of the game. Just as long as you don't do it regularly, like, every month to the same venue.
I mean, if you submit to a venue that regularly takes a year to respond, and also submit it to a venue that responds in 14 days, if the fast venue rejects it, you don't then have to withdraw it from the longer one. And if it's accepted, then just withdraw it. Caveat is that some places can be sensitive to it, but I wouldn't say most are. When you withdraw, you don't have to give a reason.
Also, it looks like AHMM *does* accept simsubs. They say:
"
Although we do accept simultaneous submissions, we ask that you notify us immediately if your story has been accepted elsewhere before we’ve had a chance to read your story. We do ask that you do not simultaneously submit the same story to AHMM and EQMM. If we reject your story, for whatever reason, you are then free to submit it to EQMM (and vice versa)."
So you are free to submit it wherever else you like, even while it sits with them.