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.