727 flex plate?

Just got back from local trans shop to help identify this combo. Their best guess is, it looks like a Vega 9" converter that had been customized with anti-balloon plate and plates welded to adapt ring gear. Positively id'd the crank. Mopar 360 cast crank. Must have been machined down to fit 318 main journals. Not sure what pistons are in there.....I guess that will remain a mystery for now.
I just ordered a flex plate from CRT for a 360 crank. I will go from there when it arrives. Not sure what I will use for converter yet.
If you ordered a flex plate that is offset weighted for a 360 it will be wrong and will cause a vibration, if it truly had no vibration the way it was. The parts in your picture are for neutral balance.

How did you positively identify this as a 360 crankshaft; casting number? You said it was Mopar. If it was a Mopar Performance crankshaft it could have had a 318/340 main size with any stroke, so you’d have to measure stroke to be sure.