Before you get into all that....if all your Quantegy/Ampex reels were playing without the rub...then it may be just that new reel. Check it against the ones you know play without issues.
If you are now going to use the ATR stuff, and all their reels line up that way and there's nothing specifically *wrong* with them...then yeah, make the adjustment.
The other thing you can do if this is just one reel....is to transfer it to another empty reel that you know works fine....and just bypass the tape guides....go directly reel-to-reel. It's a little tricky, and you have to engage the guides to make it work....but I've done that when I didn't want the tape dragging across my guides (for whatever reason). Just watch the speed....it CAN get away from you!
It sounds to me like the ATR reel is much thicker, and so it rises up higher. If that's the problem, you can also remove just the lower side of the ATR reel, and replace it with a thinner flange from another reel...assuming the screw holes line-up...which they should, unless ATR uses more screws than Quantegy/Ampex.
Other than that, I can't tell you where the two screws are for the brake drum...I'm not familiar with that deck, and your image is real blurry, so hard to tell from that.
Someone with an MS-16 will chime in......