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It seems unusual to me to have a 340 A-body with an 8 3/4 with a 3 speed between the pair.



It was actually pretty common, as the 3-speed didn't get an insurance surcharge like the 4-speed did.

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If you do change to the 4 speed The drive line is going to need to be shortened.



No, I've done this conversion a couple of times; the (all-synchro) three-speed manual trans is the same length as the 4-speed manual, so the driveshaft length is the same. As I recall, you do have to change the front yoke, though, as the 3-speed has a 904 sized/splined output shaft, while almost all 4-speeds have the 727 sized/splined output shaft.