Mine did this exact thing on the right side, the strut rod receiver cup had broken free of the subframe and was flopping around inside the bushing (My front motor mount was bad too, but after replacement the problem still existed).
You can't tell it's bad by looking at it, in fact the shop that I took it to said they were fine and it was just the bad motor mount. You just need to zip the front nut off the bushing, take the front bushing out and look, I bet you yours have both come loose.
If so you can weld them in, or get the Moog replacements.