My first thought was busted motor mount also.
An easy way to see what is really going on is to pop your hood and get someone else to start the car and put it in gear hold the brake down hard and slowly give it some gas. If broken motor mount the engine will likely lift up on one side. If the engine doesn't move look under the car. not in the way of the wheels of course, and view your tranny to see if it moves when it's power braked.

I had a 69 Olds wagon that had a broken motor mount the engine would lift up high enough to make the fan hit the upper section of the fan shroud, never kicked out of gear though even with the shift on the column as yours is.