I originally set the bed up with sisal and had no real problems with stretch once I got past the initial break-in period. I set everything up very tight and have had no problem at all with sagging. I've since strung the bed with manilla because it's actually cheaper for me than the sisal.
For around 20 years we set up a rope-strung bed when camping. I used Manila and never had much trouble with stretching. I used softwood but it was 2x8s so they didn't warp much.
I used pegs for the ropes. Originally I wove the rope individually. Later I started doing it in pairs. This sped things up a lot. I didn't have to run the entire rope back an forth. I would just run a doubled over piece, hook it over two pegs, then tighten. It worked just as well.
Mark