I don't really see any practical way for a human to write this program other than generating an extremely large number and then testing all programs up to length n for halting within this bound, in which case you've already pretty much solved the original problem.

Wait, its even worse. A human in a room is an algorithm, and as such cannot solve the halting problem. There's got to be some programs we just can't know if they will halt or not. Which means there's got to be an n beyond which some programs of length n or less cannot be analysed by humans.

That, or we have some special magic in us.