Sorry I can't be much help, but I would be willing to bet that that FMX trannie is a rare one in your '72. I'm not sure if an FMX was even available in '72, I thought by then Ford had gone completely to c4/c6 trannies. I've seen many '69 stangs with FMX's but I'd be guessing if I told you they're available years and aplications. I know that the FMX is a heavy small block tranny and that like many other ford parts it probably interchanges with a lot of years and applications. If you can find a date stamp/casting or codes that are on the case it would be interesting to find out if that tranny is original to your car.
If you need help with the codes, post another message and I'll let you know what it means.
As for the flex plate if you haven't paid for it yet don't accept it, get the correct one to your aplication. A 302 that would have come in an earlier car, if it turns out that the tranny isn't original, would have had the same balance. So if your flexplate is damaged but apears original to that engine/trans combo then order a new one. Make sure you count the # of teeth and the diameter, and any other details you observe so that the right part is obtained. If the vibration has been there since you bought the car, then the flexplate could have been replace before and is the incorrect one. This is where it would be useful to know the year of the tranny and or engine too. Check the engine on the passenger side near the back (closer to the belhousing, where the tranny meets the engine block) and just above the oil pan. If one of the codes there says D2AE... the it is most likely the original block. The other code indicates the casting date (ie: 2B24 sould be 2='72, B=2nd month=February, 24= 24th of that month)
If you could find out for sure if that tranny is an FMX and what year it is then you could probaly just order the correct one, install it and see if that works. The diferences in flexplates is, as you aready know are the balance and the diameters/number of teeth. If your eng/trans combonation now starts fine and the starter doesn't sound like it is making very obseen noises like it is chewing itself to bits. You're probably fine as far as # of teeth and diameter go. I don't know what the balance for the different fexplates is. However if the balancer is a 28 oz imbalance, I would think that, assuming every thing internal is balanced at 0 balance (weight or each rod, piston, etc is the same) then the flexplate should have a 28 oz imbalance as well, just on the opposite side to the balancer. I wouldn't recomend remocing the weight from the new/existing flexplate. This could cause more harm than good. Plus if it's a new part it can't be returned.
Just a thought: Has the car been sitting for a long time before you noticed that problem. If the car is already apart see if you can borrow another torque converter, or see if your's is balanced. Some old burned tranny fluid may have become soo stif that it actually is causing an untraceable vibration?!? Did the tranny ever get supper hot, cause the troque converter may have balooned and caused a warp. When examining your other tranny parts pull the torque converter, (the big round thing that holds a lot of oil and is bolted to the flexplate) have it checked out.
Hope this helps. Keep us informed as to what is discovered.