Under contract - 2003 Neptunus 56 w/ cat 3406e - top speed/rpm issue

Or maybe it has engine trouble. Regardless, I'd go no further until it was figured out and it turned maximum RPM.

Why?
Leaving aside the fact that the hour meter in one of the ad photos shows less than 1400 hours, I would want to know the real reason for the overhaul, because these are solid engines that at 2000 should still be barely ran in, if properly used and maintained.
Anyway, if you check out the attached specs sheet, you will see that there's nothing wrong with their fuel burn as such, because at full load they can produce the max rated power at any RPM from 1600 onward - hence obviously burning as much as if they were running at 2300 fully loaded (i.e. 40 GPH each, according to the manufacturer).
Regardless, overhauling engines and not checking that they can reach the rated max RPM afterwards strikes of a bit of a Mickey Mouse job, to put it bluntly...

I would think CAT techs could hook up laptop and figure out the state of engines. Could be props are just off. Fuel burn on older boats is often off a little. I imagine it would be 4-6k for the props to get modified.

I’d ask for the owner to get the rpms in tune but in this market he might not. Could do a full survey and just ask for some dollars to address.

Did they do a proper test and trial after the overhauls? Does the owner have documentation? If the overhauls were done by reputable CAT shop they would have flagged the low RPM at WOT during trials. What did they have to say about the issue after overhaul?
I would not proceed unless seller corrects the issue to your satisfaction. Given you do not know where the problem is, there is no telling the cost to correct. Unless the seller gives you a substantial reduction I would be very cautious here. Something does not sound right.

Stop worrying about speed and concentrate on RPM.

If properly propped, you should make full rated RPM at full load. That’s full fuel, full water, provisions and people aboard.

Stop buying excuses from owner who let things deteriorate. It's not speed we're concerned with, it's RPM.

Anyone who rebuilds and fails to see they're meeting max RPM have zero test of their rebuild. The number one tool in evaluating any major service is a sea trial after to see that max RPM is met. We regularly check all boats to see that Max RPM is still achieved. With most, you get slightly more in peak condition. 25 less might be ok. 50 really stretching it. 150 less RPM is a serious issue. While it could be prop, I doubt they suddenly changed props. Are these CAT certified rebuilds?

Ask if they used a Gold or Platinum Kit?

May be certified techs, but not a CAT dealer. (I checked CAT's site). Claim to specialize in CAT. I have no experience with them. Don't even have a website.

3406E-800's on a 53 Convertible fresh out of the slings with a perfect bottom, perfect props, and very light on fuel as well as water. WOT sea trial...

Full of fuel and water she would turn at or just shy of 2325. Sharing the data for you to compare.

Perfect, exactly what one would want.

Bad manifold temperature sensor on stbd engine, possibly?