Okay Pancho, I'll take your word for it, but I think you may have dampened out a harmonic, and that is no substitute for getting things mechanically (physically) into spec. If you have a rumble back there at the strut, it may be a worn bearing or a misalignment, or both, possibly caused by a misalignment.
LOOK at your shaft when the boat is moving, and you will see quite plainly, if you have any movement in the shaft. If you see movement, you found your problem.
As for the shaft size, I can't help you on this particular boat, but if it's a 37 I'd think you have a minimum of 1-3/8 and more likely a 1-1/2, but your notes say 1-1/4???
Good luck,
Tom
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