First time using a form like this but by now I’m desperate. Still too stubborn to give up though. I replaced both rear drum brakes on my 07 Taurus (FWD), the old drums were a royal pain to get off, bent up the backing plate a bit, that’s been fixed I believe. Put the new brakes on, lots of pictures and double checking, they’re on right. Get going, there is a rhythmic grinding, it seems at random but I’m not really sure yet. I get the thing back in the air take a look, I straighten out the backing plate a bit more, still does it. The wheels have noticable resistance to spinning when it’s in the air, again rhythmically. First and foremost, is it dangerous to drive on? Second, will it fix over time or did I screw something up that needs fixing?
There’s something obviously wrong and no one can tell you if it’s safe without seeing it. If you fought that hard getting the drum off, there’s probably a good size ridge on the drum. This should be turned off or replace the drum. If the hardware is installed and lubed properly you should be able to see if it’s rubbing on the outside of the drum. If you know it’s not on the outside, then it’s on the inside, probably the ridge.
It sounds like your drum is out of round.
The friction surface on new brake drums are not polished, you may hear a mild rubbing sound, especially if you adjusted the brake shoes too tight. The rhythmic nature may indicate that there is run-out in the drum, it may or may not be excessive.