Geezer here: having written "Iolo's crossbow book" I believe I can comment authoritatively on it. For the lightweight crossbows I build, (maximum 200 lb draw) I generally use 11/32nd standard arrow-shafts, cut to approx. 15.5 inches length. Spine weight doesn't really matter for the shafts, but I suppose you could get shafts that were just too wimpy. Getting shafts all the same spine is a good idea.
I generally fletch with two, three-inch feathers, spun clockwise (not that the spin direction matters, just so they're all the same) For heavier bows I use 125 grain heads... 160's if I can get them for the strongest bows. For my lightweight bows, I prefer 100 grain heads, and have made up target bolts with 70 grain heads and 5/16th inch shafts.
Extant medieval bolts I have seen vary between 12 and 18 inches long overall, but seem to average around 15 inches in length, and 1/2 (12.7 mm) and 3/4 inch diameter. Some bolts may actually be oval in cross-section, being slightly thicker top-to bottom than side-to side. Shafts are of hardwood, with ash being preferred for strength, but birch and oak are also acceptable (honestly, you all suspect the fletchers used whatever they could get, don't you?... yeah, we're on the same page here) The medieval bolts I have seen that still have their fletching use thin, flexible strips of wood set into the grooves in the side of the shaft... fletching about 5 inches long.
Butts of bolts are flattened into an oval shape, full height of the shaft, but only about 5/16th inch wide.
Mostly the shafts look more or less parallell, but some do seem to be slightly barrelled as Payne-Gallwey shows 'em. No doubt there were special target bolts of odd shape, like the fluted/unfletched 17th century bolts PG shows.
It's good to be back. Geezer.