The pertinent question seems to be: What do we not know about period bowstrings that allows them to support the draw-weight of these bows?
The only question I could ask is are they glued or waxed? If so, is there a difference?
I found out in conversation that italian hemp is better than, say, english hemp, as an aside from one of the guys I know who makes reproduction fishing boats and likes the 'real thing' rather than modern nylon type rope. You can still buy this, so stripping a piece down and trying it with glues and wax in a set size string would give a decent guide to breaking strains. Any experts on medieval glue making??? I am guessing cobblers wax would be ok, as well as straight beeswax to see if these give any variance.
Going through my MR book( weapons of war vol1), pages 636/637 also refers to hemp and silk and gives knock sizes that would allow a 3mm string, so that seems a reasonable size to pick.