I think I was very lucky here. I drove over 300 miles since the problem first became apparent.
The strange vibration and thunking recently exhibited by my 84 240 are no more. Turns out it wasn't the tranny mount, but BOTH motor mounts had broken completely off. The engine was resting on the frame with a slight angle to the passenger side, causing the "growl" when I turned right and the starter thunk.
When I looked at the mounts from under the hood I couldn't see they had come apart. The rubber was mostly intact, especially on the left-side mount by the oil filter which blocked my view of the bracket.
As a total noob to this issue groping around with my hand to check did nothing to alert me either. I had the tranny mount replaced also, since it was looking all of it's 19 years of age.
I think at least one motor mount was broken when I bought the car, since it now is so much smoother and quieter over bumps in the road than it ever was before.
Total repair costs for the 3 mounts: $23.50 for parts, $96.00 labor.

My only fear now is how long the mounts will last, since that the parts I bought through FPCGroton were from Scan tech.

Thanks to all that replied with their as usual right-on-target advice!