Alm's "Survey" is a very useful book, but perhaps not $320 worth, unless you're rolling in dough. The Harmuth book is also a treasure, but since it's been out of print since 1986 or so, it's also sky-high to buy.
Paterson's book will help immensely, and it's reasonably priced.
George Stevens "The Crossbow from 35 years With the Weapon" is very useful, particularly for people who want to build more modern crossbows. It's horribly laid out... the editor should probably be shot... with a crossbow of course, but there's good info there.
And take Mac's comments to heart about Payne-Gallwey. By and large, he tells you what was known (or suspected) in 1907, when the book was published, but there's been a lot of scholarship since then, so don't be too surprised if Paterson or Harmuth or Stevens disagrees with him.
Payne-Gallwey does have a lovely set of drawings for a 15th-16th century Flemish arbalest. I have a couple of quibbles about that too, but basically it's a solid design. Geezer.