360 LA using 904 Tranny

I did the same swap about 10 years ago and purchased a hi stall TC from Pat Blais (torqueflite Patty) on ebang. No need to change out the flex plate. I only see a 62-67 currently listed but you can give him a call. He is a stand up guy and the price was reasonable. No issues.

Torqueflite 904 1962-67 Rebuilt High-Stall 10-3/4" Converter - 1.55" CRANK PILOT | eBay

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He needs the larger crank pilot size, 1.810", not the earlier small one. He hasn't said if he is wanting a high stall yet. From the factory, the 360 had two stalls, a low stall at around 1900-2000 stall and a higher stall one that could stall about 2200-2300. No mention as to what if any engine performance mods have been done.