Soo... I took my '68 350 HO to a local shop where I know the guys to look at a couple of items. On the hoist, we found an oil pan gasket leak and noted that the oil pan is literally sitting on the cross member, The engine was rebuilt by the previous owner and included new motor mounts. The guys at the shop figured that the new motor mounts didn't have as much clearance as the originals and they could add some shims. Also, I was told that in order to change the oil pan gasket, they needed to pull the engine,

Any thoughts on this?

My 69 was same way with 2 engine
when I bought it the engine was sitting on cross member
I didn’t think much of because of the age of car
When I put the new engine in with new mounts it did the same
I did some looking and found that this common
now I was told between years and aftermarket oil pans the way they were shaped changed slightly
You can try different brands I even tried mity mounts they didn’t work
I used the shims 1/4 thick worked for me I also have aftermarket chrome oil pan now pan sits above crossmember
Butler Performance has a nice selection

Yes the engine dose have to almost come out you can try to lift engine up and try to get it out past the main bearing caps and below the trans
But some engine you just don’t have the room to do this
Good luck with car

Butler performance has a 1 peice oil pan gasket which is metal coverd in lined rubber
Check their web site out

Butler's 1-piece gasket comes from BOP Engineering who developed it about 10 years ago. Which was just in time for me to pull my freshly built 455 engine to fix an oil pan gasket blowout caused by high ring blow-by.

Definitely a nice piece of engineering.

Rather than put shims in, maybe try new motor mounts?
There isn't a lot of clearance.
If they are lifting the engine for shims, might as well replace the mounts.
No need to "pull the engine" just lift it up to clear the crossmember.