Question on 360 crank balance

No. No, no, no, no! If it's still the factory LA 360 external balance, then you need the factory 360 balance weight on the convertor with the factory flexplate (notice how all things I mentioned are "factory"?). If you use a non-360 (internal/neutral balance) convertor, THEN you need the B&M flexplate. The one you mentioned is for a 727, a 10239 would be for a 904.
You sure this guy has dealt with Mopars before?