Wow, this was very finicky!
I refused to solve the problem manually. It was clear to me in the morning that it’s not tricky in the algorithmical sense, but that there will be many fine-print details to pay attention to.
I ultimately solved it in a brute-force fashion. I did a depth-first search to find complete paths, then on each path I look for a valid program. This boils down to trying all possible triplets of main routines until I’m able to encode the entire thing into three routines, none of which exceeds the desired length.
The code is available here. It could use a bit more of a cleanup, can’t say it’s my finest hour 
