Thank you so much for that, as it seems to have been the answer. I followed your research, and after realizing that using the word "restrike" would get me where I wanted as well, learned a fair bit. So, to the best of my knowledge and based on an educated seller's listing, I think this is best labeled as Scheiz-Zurich Thaler 1559 Restrike by Lauer 19th Century. 23.3g.
I found a bit that noted these were made of white metal, not silver, and most of the ones I found came in pretty close in weight to the one I have. Also, along with a perfect die match to the Lauer restrikes, I learned that they actually came as jewelry, not a coin. That means they all originally had a clasp at 12:00, and sure enough, looking at the edge of my "coin" I found remnants of a clasp that had been sanded or filed off but still quite obvious.
So I think that closes the door on this one, which based on the one sale I could find with it correctly listed as a restrike makes it about a $40 item, and perfect for my counterfeit collection.
Thanks to all who commented and especially tdziemia for such valuable help.