From what I read last season, a reason not to have too many bines on a string is to allow enough air and sunlight in to keep the leaves from trapping too much moisture, which promotes disease. The recommendations I've always seen were no more than three bines on a string, and to spread the strings out by at least a few feet.
For my first years, I only ran the one strongest bine up each string, and the strings were on ~3 foot centers, and then once the side-arms appeared I trained them up the strings with the main bines. From all appearances none of my plants developed any issues, and the production was pretty amazing for first years and a single bine per rhizome.
This being the second season for these plants I'm planning on training the two strongest bines per crown up a single string...
Cheers!