I really have to wonder what he's doing in his C functions that the stack model is a problem. Most of mine are very simple: pop some values, maybe read some table fields or pcall a function, then do whatever the C function actually does, and push some values back. Yeah, lua_settable is a little awkward, but how complex is your code that calls it?
After a very cursory scan, it appears that he's shadowing a lot of standard Lua functions to provide his own versions, like a replacement for ipairs that checks an __ipairs metamethod first, that sort of thing. It doesn't actually look that complicated to me, but I've also done a bunch of embedding-Lua-in-stuff projects before.
