Nobody else has chimed in, so I'll share the little bit I know. The best bet is to scour Ebay, craigslist, and similar places. Call or email Sheaffer tractor (Lens12 here on TBN) and see what he has. Tractor recycling/dismantling yards may have one.
There weren't many machines built that had reverse rotation PTOs (The Kubota
B6000, your version of the Beaver, and, apparently, some obscure Iseki machine) and were designed to use implements matched to their PTOs anyway, especially tillers. These small Japanese machines were originally engineered to run tillers in small rice farms, so do that job exceedingly well. There are tillers designed for the
B6000 and your S370 that take the backwards direction of rotation into account. Consequently, the reversers are out there, but they aren't a "normal" item.
As a last resort, a retailer in Belgium sells them for 720 Euros, plus, obviously, trans-atlantic shipping.
Yenibiz en Detail PTO reverser
As a last-last resort, I suppose one could get a fabrication shop to build a replacement auger, designed to rotate the other direction. It wouldn't be THAT hard to do with the proper tools, and may be cheaper than a reverser anyway.