S3 E-Type exhaust manifold stud replacement

When I bought my E-Type 20 years ago it was obvious that the owner had hit a speed bump too hard, since two of the exhaust manifolds were broken. I dug my way down to the manifolds and replaced them, but the lower rear nut and stud on the left rear manifold was missing. When I took the manifold off I tried to screw in a new stud, but it wouldn’t go in.
It appears that the stud is sheared off, since nothing is protruding from the head. There was no way I could do anything about it since it was the rearmost stud and located somewhat within the transmission tunnel. I put a new gasket on it and drove it like that, with one fewer stud holding on the manifold.
Last fall when I ran the JCNA slalom the exhaust was leaking so badly from that cylinder that it sounded like I was about to throw a rod, so during the winter I removed the manifold again, along with about 8/10ths of the gasket. The rest of the gasket had been eroded by the escaping exhaust gases. I got a new gasket, slathered that area with muffler cement, and bolted it back together, hoping the cement would fill the gap and give me a little time. Well, it’s starting to leak again, and this time it is very obvious since I had also replaced the exhaust system while I was in there last winter. So it looks like I will need to replace the stud somehow.
Finally we get to my point, and why I need advice from those who have gone before. There is no way for me to effect a repair while the engine is in the car. I can think of a couple of options. One is to remove the engine and work on it while it sits on the floor. I have a 2-post lift, so I imagine I can remove the carbs and exhaust manifolds to make the engine narrow and lift the body off, leaving the engine on a dolly. However, there are a lot of other things attached to the engine that would need to be disconnected before doing that, and I don’t know if the engine mounts would allow that anyway.
Another thought is to remove that head and work on it on the bench. That way, if worse comes to worst I can bring it to a machine shop. Working on the bench seems a lot simpler, but taking the head off in order to put it there is where I have questions. I am familiar with the XK engine, to the extent that I pulled the head off my MK2 last winter just so I could polish the aluminum and paint the valley. However I am not at all familiar with digging into the V12 engine, and that’s why I need advice from those of you who have experience with it. I am able to borrow a head puller from the JCNA tool loaner program, so that is a help, and it looks like I can pull the head while the engine is still in the car (?), so I’m leaning in that direction. Does anyone have any advice for me, one way or the other?

@MarekH, this seems like up your alley.