There's probably a misunderstanding here: Of course I'm not intending to have the C function continue where it left off. This is obviously impossible. I just want the C function to be called again. The C function code will always be run from its entry point, not from somewhere in between.
You'd be better off switching to Lua 5.3, where you can use lua_yieldk to specify a C function that's called on resume. This function will find the Lua stack as you left it, with the results yielded replaced by the arguments to resume.
I have not used lua_yieldk much, but I do use lua_callk an awful lot so Lua code can call C code that then calls Lua code, which can yield if it wants to.
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