Will the retractions ever stop?

So, here's where I am with regards to leather now:

Most sources on fat-cured leather, mostly relating to Native American brain-tanning, indicate that the the grain side is normally scraped off before the fat is applied.  It does not have to be, and obviously cannot be in the case of furs, but doing so does allows the hide to absorb the fat much more readily.

The upshot is that contrary to my previous recommendations, prior to the introduction of veg-tan, the leather available to the Persians and other ancient West Asians most likely (or most likely usually) did NOT have a smooth finish.  Rather, it may have been lightly napped or sueded.

Just to be clear:  It is possible that smooth leathers were available or even common.  It's just that given my current understanding, it's unlikely that they were common.

Therefore, my recommendation is that you look for any of the following:
True brain-tanned - available mainly from small craftspeople.
German-tanned - deerskin cured with cod liver oil.
Double-sueded cowhide and splits - mostly chrome-tanned.  Look for those labeled "glove-tanned" for the softest texture.

If you have only "commercial" buckskin with a grain side or smooth glove leather on hand, you can just turn it inside-out as long as the flesh side has a fine nap.

The sources available on the Internet are endless, but off the top of my head, a few in the U.S. would include Crazy Crow Trading Post (German-tan, commercial deer and bison splits, and cowhide), Tandy Leather Factory (pigskin and cowhide splits - I don't know about the finish on their deerskins) and Braintan.com.  All these companies also sell rawhide.