And one more refinement to the chain idea...
In almost every rigger's tool bag you'll find a foot long piece of bicycle chain. It is usually easier to thread down the mast because it only bends in one direction.
While running the messenger line, keep all the other lines in the mast tight. That reduces the chances of a wrap of one around the other.
If you can heel the boat over a bit, the chain runs down the wall of the mast and, if you have lead a good and pure life, just falls out the halyard exit. For some reason that rarely happens to me! Once you get close to the exit, a strong magnet can help guide the chain to the exit, unless you used good stainless chain...
If you haven't lost a halyard, you just haven't lost one YET.
Fort Lauderdale, FL, USA