Geezer here: I've been following the discussion about bound-in prods (laths). There have been some interesting ideas mooted about, and Mac's careful drawings of the binding process, as well as his observations about lashing on stirrups are particularly insightul. Indeed I expect no less of him.
From my personal experience with binding in crossbows, I can offer these observations, with a caveat or two. These days I use heavy hemp twine to bind in bows. There are several suppliers online that can offer 3 to 5 mm cord, which is about the size you see on medieval pieces. I think flax (linen) is stronger, but hemp seems to be most common in extant medieval/renaissance pieces. Of course I do the cinching-up along the sides with artificial sinew, in a pattern of my own devising. If you see a row of knots atop an artificial-sinew cinch, it's probably from my shop. My system works for me, but I've never seen that row of coxcomb-stitches on a period piece.
I have noted that most of the pics in our group show the binding strung through a simple round hole drilled through the stock (@3/4 in dia.), and indeed there are a fair number of medieval pieces that are done so. A better system shows up in a lot of German bows. Drill the requisite hole, then flatten out the front portion, so the passage assumes a "D" shape. Then round of the flat surface of the 'D' so the string doesn't cut in to the stock. Some very strong bows actually reinforced the flat of the D with blocks of horn to reduce wear. If you make your binding-hole this way AND you crank it down as Hard as you Can, your bridle/binding cord should stay tight for years of service.
Of course, fixing it with wax or glue or whatever, may help extend the life of the bridle and make it more water-proof, but the 'D' shaped hole really does help. Geezer, signing off.