We ran the engine torque test at the shop, resulting in diagnosing the front transmission mount as the problem. After replacement didn't correct the issue, the shop re-ran the same test (while I watched) and observed all other mounts, none of which seemed to be out of order. The bearings don't seem to have any play at all, neither do the ball joints, stabilizer bar ends or tie rod ends. When the event happens, the entire front end of the car can be felt to wobble side to side, seemingly on both sides. It can be felt slightly through the steering wheel but more so in the entire front of the car, and even pulsing through the gas pedal. The wobbling is accompanied by a "thud, thud, thud" noise that gets louder the harder the acceleration. As soon as the gas pedal is released the event will end and car rides like new.