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It would be best to ask the balancing shop this question since they did the work. Especially since you say they internally balanced your 360. That is a very expensive process where "Heavy metal" is added to balance the assy. A Regular balancing job does not include this and costs much less.
When I had my 360 balanced I used the B&M flexplate part number BMM-10236 (for use with a 727) but my 360 is still externally balanced. The convertor used is then a neutral balance converter.