it is to align the bones of the bow-hand parallel to the bones of the forearm, so as to give a much more solid launching platform than is possible using a symmetric bow (which invariably cocks the wrist off-axis)
it has the side benefit of reducing or eliminating the bow's recoil: because of the weight imbalance, the bow (if held properly) will pivot in the hand instead of boinging back and forth.
as to its asymmetry - not just in its recurve profile, but in the tapers side-to-side and front-to-back. These tapers are VERY subtle, and you must examine the in-process bow very closely to make the correct determination.
I'm fascinated with your project.
Begging your pardon if you've posted one already, but have you any links to pictures of what these kinds of weapons typically look like? I thought I had a good image in mind, but the details you gave in your most recent descriptions don't mesh with my previous mental picture. I see a general recurve bow form with upper and lower sections offset fore and aft of the grip to allow the alignment of the wrist that you described, top section forward, lower section aft. But is the assymmetry just that, or are the two ends of unequal mass, as well?