Back when I was playing SCA, I used to sing pretty much whatever I bluddy well wanted, so long as it wasn't obviously "modern", plus a bunch of my own stuff and "SCA-Traditional" local pieces. The audiences liked it, although of course the purists looked down their noses at me. That's OK - I've found in SCA the peasants have better revels and are more generous with the libations than are the Royals or Laurels. But as Foolestroupe observed, I eventually got fed up with the negative attitudes and the growing disrepect from attendees at events (just speaking for myself here - your local group may be different) and left.
Anyway, one way to keep the "period police" happy might be to get familiar enough with the forms of various acceptable music & then write your own "in a period style".