All theories are welcome, high and low! 🙂

Put a 1" (25mm) tube into the coupler after engine and transom assembly switch to make a rough alignment before doing the final one with correct alignment tool. This is what I'm looking at, the engine is off sideways.
I'm going to try to push it sideways in the front but the rear mounts are in place with bolts through (not tightened up yet).
Boat has 300 hrs (sea ray 2001), never been sunk, transom sounds firm when knocking, boat has a history of vibrations so just installed a new transom assembly and a "new" used engine because vibrations damaged both. Never rebuilt transom.

Has anyone seen this much misalignment sideways before? What caused it?

This might sound stupid but have you turned the engine over by hand to see if that tube moves side to side?

Actually haven't yet, I'll do that thanks. The old engine and transom had similar misalignment but ripped those out before trying to fix it. Was surprised to see the same issue with new engine and transom assembly.

the two engine mounts on each side that mounts to the stringers have slots in them for adjusting the twist. Loosen them up and move it to where you need it then tighten back down. I have over 35 years mercruiser tech. Thats more than likely it

I don't know what you're trying to ask here. Your rear motor mounts aren't tight and you need a front motor mount. Just by tightening bolts up, it's going to shift to position of the alignment.

I have front motor mounts, had nothing to do with this really (edited the post). Well you have a point, I might have jumped the gun before ruling everything out, just that the old setup had the same shift to the side and now the new one has the same. I'll know in a couple of hours if there's room for 3/16" sideways play on the rear mounts by just tightening the bolts. But I find it unlikely.

I'll go and try right now, thanks for the tip. I'll report back in a couple of hours.

Well, if the alignment was off and they managed to cram the drive on, that could possibly explain the vibration....

Managed to move the engine quite a bit to the side on the front mounts and the side alignment got a bit better. But its still off center. Going to try to remove the rear mount bolts entirely just to see if I can get it centered at all, with all the mounts out of the equation.

I strongly believe this has been the case. Previous owner replaced the coupler two times, and the orifice on the old transom assembly, where the gimbal bearing sits, had been worn out to the point that a new bearing could be installed and removed by hand.