360 LA using 904 Tranny

360 engine: 904 converter from the factory has two weights. Both the same, measure 1.62" x .75" x .380 ", and there is also another that has a single weight.
Converter rebuilders have a converter balancer for a reason. Have you checked out getting a rebuilt 360 converter? It may be cheaper than the B & M flex plate and will be balanced properly. Just a thought.
Do it RIGHT once.