I’m staring at my object tipped over to the side and holding SHIFT is snapping it but the wrong way oriented.
Did you check what selection you have on for your rotation?
If you go under your transform section, there should be little buttons that has circle arrows that says xyz, x, y, or z.
some time you got too give a little help by rotating the model just a tiny bit in the direction you want it to rotate and while its still rotating
then>hold the SHIFT key