Tom,
I have heard that a Wickliffe 76 falling block would be big enough for a .577 conversion. I don't know for sure but I believe I read that on one of Ed Hubble's posts about some of his big calibers.

Tom Ondrus sold a bunch of them several years back as kits, there may still be one or two out there that never got completed. The action is large enough but I'm just not sure about clearances.
I also know that when the action is properly heat treated, it will be strong enough, they made a few of these in .338 Winchester magnum caliber.

The main problem with doing a .577 singleshot is that you will have to leave the barrel very large in diameter and length in order to have enough weight on the gun to help fight off the effects of the recoil. The doubles I build weigh 12 1/2 pounds, finished weight, and a single would have to weigh at least 10 1/2 to 11 pounds in order to be shootable with full loads. If you go under that amount with full loads you will pay dearly for your mistake.

You could always make it lighter and shoot a somewhat reduced loading in it BUT, some day someone else is going to come along and see that it is marked for .577's and shoot a heavy load in it. This can happen even if the loading information is stamped on the gun, (there are many out there who either don't know, or they don't understand), what they are seeing. Turning down the barrel too much could also cause a catastrophic failure.