You may not need to actually take the support out. As I recall on my 80 it required just taking out the two top bolts on each side and loosening the the ones on the bottom. Then the top could rotate forward about 1/4". That is all it took to get out - still tight and two people makes it way easier. But then be careful when you put it back in. At the top of the support where they spot welded the parts together the "flash" around the spot welds sticks out a couple mm's. Again, not much, but enough to punch through a copper tube if it bangs into it - speaking from experience. 

Well, I did unbolt the core support, and got the shroud out that way, but it was still very tight.

Update:  I reinstalled the radiator, shroud, and core support as a unit yesterday, and it was almost easy.  I had another person helping.

Interesting, never thought of that option. Perhaps I’ll give that one a try on my next radiator endeavor !!

Radiator replacement was the first thing I had to do as a new Corvette owner on my '76 18 years ago.  Getting that shroud out was extremely frustrating and I didn't have C3VR back then to help.  Unfortunately, it ended up breaking but it turned out OK - I turned it into a two-piece and haven't been sad once about it and it sure is a lot easier to get it in and out now.  It broke on the top pass side and when I got it out I cut it down the middle on the bottom.  At that time I worked for a company that had aluminum fab as part of its business and some guys in the shop helped me fabricate splice plates to bolt on to it.  Painted the plates flat black and you really have to look to notice they're there.