My Ashbory is still in the mail, but I'm jumping in anyway, because this is something I know about. I played the lute fairly seriously once, and one of my main instruments is the viola da gamba, which also has tied frets. On viols most people use a different knot, with doubled string, that makes a wider fret. I think I have a picture of the knot somewhere. Gamba players usually use old strings, and often graduate them in thickness up the neck.
If you don't have old gamba strings lying around, you can use monoflilament fishing line - I've got 40lb test on my gamba right now. The trick is you want something that won't wear the strings out too fast, but you don't want the strings to chew up the frets either. When I switched from gut to Perlon strings, I started chewing through gut frets so I switched to nlyon.
Another nice thing about tied frets (I may try them on my Ashbory when it arrives) is that you don't have to put them on all the way up the neck. The gamba usually has seven, and above that you play without, nice for vibrato on high notes. There's a local bass guitar player who had his custom bass made with seven frets - so he can get that singing tone in the solo register, but the clarity of frets down low. It sounds good.
EDIT: okay, I've got the Ashbory. I love it. If I can ever get it out of my wife's hands again (she loves it too), I may try a fret or two, but my first thought is that those soft rubber strings are just going to moosh into the fret, so (if it doesn't damge the string) the fret is just going to be a marker anyway and not affect the sound much. And the neck already has markers. The story may be different with the polyurethane strings I've ordered from Road Toad.