I've checked my LE special order 4513TSW, 7-round variant and the grip does not move at all.
When you had the grip off, did you check to make sure your sideplate was seated on the pin and was not broken? How about the two plastic shelves on the inside of the factory OEM grip (they slip onto the front strap on either side of the grip), were they intact?
Very strange that you still have this problem even after going with a second different factory grip. But if the Hogues went on and solved the problem I guess your frame is ok.
I like the Hogues better for shooting anyways. But the factory grip should go on properly regardless. Not surprised that s&w did nothing. I am surprised they didn't suggest you buy an m&p.
Regards 18DAI