Yes, it only takes an input shaft swap to create a SBF tranny, (disregarding the output shaft) but the input shaft must match the ratio of the tranny. There were only 2 ratios, a 2.32 close ratio and the 2.78 wide ratio. Easy to determine which ratio you have by counting the # of teeth on 2nd gear. You would have to do a visual to verify the BBF shaft. Don't ever rely on the production #'s found on the side of the case as all early toploader cases are identical short of that little metal ID tag.
Lots of 390's came with 4 speeds and they have the short input shaft, and yet the remainder of the tranny is the same as the SBF--28 spline output shaft. The clutch disc would be the same. The larger cube BBF would/should have the larger 31 spline output. You do not have to worry about that end since you already have a driveshaft hooked up.
As I said, it is a shot in the dark that this is your problem, but it seems like you have covered the normal items.
Another thought, you might want to take a dial indicator and check the run-out of the new flywheel as it is installed on the back of the crank. Not sure of the exact spec, but I would expect it to be something less than .010".