Hi Clayton-
Good timing! I just recently asked a similar question. Instead of copying all the responses here, I’ll link to it.
Also, if you want more information on the legality of what you can and cannot do, I highly recommend you download Chapter 7 of the book "Rethinking Our Centralized Monetary System: the Case for a System of Local Currencies". A George Washington University professor spent a summer grant doing comprehensive research on the legality and viability of local currencies. He outlines an incredible amount of detailed information, including dozens of court cases outlining what is and isn’t legal. You can find it here:
Chapter 7 - Rethinking our Centralized Monteary System
According to that book, I find nothing stopping anyone from launching a non-coin, paper money system, except for one small detail. It is a criminal act to offer paper money worth fractions of $1. This means that you can’t offer paper money that holds value better than a dollar, so essentially you’re bound to the inflation of the dollar by the Fed.
Admittedly, I haven’t read the rest of the book yet, and there is one chapter in particular that describes how to deploy a local currency that is not pegged to the dollar. I’m very interested to read what the author has to say about non-pegged local scrip.