Update

Got the oil cooler off. It was a pain in the butt as I dont own a 46mm socket to get the filter housing off.

I realized when I got the cooler off that the coolant and oil both enter the cooler... duh. For some reason I thought it was pumping coolant into the cooler and cooling the oil that was inside the filter housing. Also of note, the gaskets were completely fine. Both were set in tight with no noticeable signs of wear. These gaskets would not affect anything besides oil leaking to the outside of the engine anyways.
When I took the cooler off I dumped it out in a bucket. While doing so I saw what seemed to be fairly fresh oil come out of the coolant side, leading me to believe this in fact my problem as told by the mechanic.