While low sustain is a factor, compound bows are also more efficient and powerful. They have more rigid limbs and the pulley system spreads the weight further over your draw. Quick googling suggests compound bows are around 50% more powerful, gaining an extra 100fps or so over standard recurve bows, which also makes me wonder why the compound bow ingame is such a piece of junk. They clock in at around 300fps, the same as most crossbows.
From what I can find, it seems most compound crossbows are going to manage an impressive 400fps, the same extra 100fps that a compound bow has over a recurve, which is a fair bit of extra power. I’d expect one to be pretty powerful ingame, and I’d expect certain hunting or mechanical books to provide enough information to make one yourself, although the materials used are usually pretty high end. You could even modify a compound bow into a crossbow if you wanted to I suppose…
Most of those numbers are from high-end, modern, professionally made weapons though, so our handcrafted ones are going to be a bit weaker. Still, a compound crossbow is going to get a good 30-40% extra speed, thus damage, on a wooden crossbow, and the current compound bow should be much stronger, at least on par with the reflex recurve, if not stronger, albeit maybe not as quick to fire. I can’t find anything on reflex bow speed though, so they might be a little tiny bit faster than a recurve. Maybe.
(All numbers are, as mentioned, from quick googling. Though I do know from personal experience that compound bows are substantially more powerful than recurves.)
A windlass could still conceivably pull the pump handle, or you could just hook a small electric air compressor to it.