Troubleshooting running gear vibration

Can you marrow down when it started or is it how you found her? From what you describe it sounds like it doesn't impede running, so it's possible your delivery crew chalked it up to an idiosyncrasy of the boat or it was disguised by the PTO issue. Otherwise they sure should have mentioned it. When your diver went down did he bring a straight edge to check if the prop was true? From there it could be anything from the prop to the motor mounts. Without hauling all you can really check is the mounts to the shaft log and my rough guess with what you describe is that the problem is outside; prop, strut, cutlass bearing, shaft. If you're lucky there's something wrapped on your prop but I'd think your diver would have seen that unless you picked it up after.

That exhaust is a good tell-tale that would point me towards the alignment or mounts. That should be a rubber plate although it could be separate bushings. I've been on a couple boats when the engines were realigned and it seemed a matter of trial and error, but maybe someone who's actually done it can chime in on that. In the mean time maybe you can have your mate watch the gap at the mounts and compare the movement.

It could also be something internally in the engine such as a bent rod or dead cylinder, etc.

Instead of poking guesses on an internet forum. It would be best to just hire a good CAT mechanic that's good with vibration related issues.

I think that would show across the entire range and worse at the top end.
Hiring a mechanic is most likely where he'll end up, but I've always found that if you can narrow down the source of your trouble it's cheaper to resolve. Plus it'll help the OP learn.

if it’s got underwater exhaust, a good chance it’s coming from there too

Which part of the Bay Area is the boat sitting?

I have the boat I'm buying on the hard there now. I have been impressed by the yard in general. I only needed bottom paint and prop shaft seals done so I cant vouch for the veracity of their mechanics. They do allow outside vendors and owner maintenance and access to the boat 24/7 which is really great.
I had Cummins on my last boat and Volvos now so I don't have a good referral for a Marine CAT mechanic for you. It seems like everyone I know with larger vessels are running Detroit's. Good Luck and if you find yourself in Benicia look me up on B DOCK.
Rusty

You also eliminated the motor mounts. When you take it out have someone ride the engine room to check the transmission, shaft, etc. Maybe video corresponding spots on both engines while it's happening. That way you'll know if it's outside or in before you get to the yard. That exhaust and it happening at a specific rpm really makes me wonder though. I get the feeling it's inside, probably alignment. We had a similar situation on a boat I ran for awhile. Didn't make much of an impression on me cause it wasn't debilitating, just an annoyance. An idiosyncrasy of the boat, which would explain your delivery crew not mentioning it. Seems to me we had a mechanic chase the alignment the whole summer and I don't remember if he ever got it right. Long time ago.