Have there been any published estimates of the relative rarity of the various mints issuing coins between about AD 300-350?
Don't know the precise answer but there is a database collecting all the known examples of the 313-476 CE period here : http://www.nummus-bible-database.com/ In french, but easy to use with a few keywords in mind. At the moment a bit less than 60 000 specimens are referenced Hope that helps Q 50+ coins of mine are in there (small contribution )
That looks like an excellent database from which to do a little original research. Thank you @Cucumbor