Engine swap maybe?

You did mean 60°, right?
The 5.3L LS4 bolt pattern is the same as the 2.8, 3.1, 3.4, 3800, and 4.1/4.5/4.9 caddy.
Except the start bolts to the bellhousing at rear left side of the engine. I've got one and did a trans a year or so ago.
You'll also note that the lowest hole on the right isn't threaded. The bellhousing is and you have to remove that bolt entirely by feel on a 36" extension from the passengers wheel house. Don't pull it out. Just leave the threads in the block or you'll be hours trying to stab that hole again. It's between the block and the trans and can not be seen.
The FSM says "remove bolt #6". Fortunately I found a You tube video on how to reach it and to not pull it out before I started the R&R. You actually have to remove the entire front subframe while supporting the engine from above. 2 days in and out and then had to have it aligned.

I'm confused. What was causing this "gap"? Unless you pulled the intake manifold, nothing should have changed there when you made this repair. It's not uncommon for the intake to appear to not line up with the head where they join, which is why they are notorious for leaking. (I got a fix for that too), so don't assume that if they don't line up that it's because they aren't at the base. Now, that being said, when you put a new manifold gasket on, it's imperative that you make sure that the intake is completely flush. It should have guide studs on each 4 corners to ensure that. The intake MUST be torqued down a bit at a time to ensure that the pressure is even as it goes down. There is a sequence. Many, many years ago as a young guy I somehow missed one of the bolts on the old 2.8 and it was getting coolant into the block. It's easy to screw up.

Now, if you have not touched the intake during this repair, my guess is that what is really happening is that timing cover/water pump housing isn't sealed well or that seal has become broken. It's important to note that a couple of the bolts that pass through the water jackets there hold the water pump on. There is a brace you can fabricate (in the Haynes and other manuals) to keep pressure on those two areas so that you may remove the pump without removing the front cover. If you just start jerking on the pump without that brace, you CAN break that seal and allow coolant into the engine. If you started getting coolant in the engine after this kind of repair, I don't think the intake is or was your issue if you hadn't touched it and there was no water in the coolant before. Also it's a good idea to put a little RTV on those bolt that pass through the water jacket. No globs. Just a little on the threads.

And remember, the 2.8 family is a 60 degree V6, so the smaller angle is why the head interferes with the intake. That's just by design.

Hope this helps.