You are probably so close.........
On one fit up I did that required facing the breech and deepening the pivot did just as you seem to describe; it wouldnt hardly catch and I had to, ever so slowly, fine tune the pivot to get the breech to 'settle in' just a tad deeper. I was fitting a .22LR swap barrel into the .22 Mag so I had the original barrel to switch in to see how the .22LR barrel was still up a little too high in relationship to the standing breach. This kept the latch from engaging the shelf.
I have to wonder why you tried a shim on the pivot when the 'headspace' was already tight? Well, anyway, you saw that made it worse, right?, so that isnt the way to go.
When you get a little engagement happening it will probably start to make more sense. I like to fit fairly tight so the parts can work in under stout closings and actual firing pressures. Quite often all that is needed then is a tiny bit of final tuning, if at all. If you fit it up too loose it wont ever get tighter, kinda like the woodworkers joke,'cut it off twice and its still too short'.
BTW, are you doing this fitting with the extractor/ejector out? You dont need it giving you any false signals. No need for it there until the barrel fits right anyway.
I am way leery of changing the latch shelf other than maybe a couple of light strokes from a fine stone. It is easy to think of that spot as the solution, but, IMHO, it is not.