Chord Shapes (downmajor tuning)
Chords are named using ups and down notation, see also the notation guide for edos 5-72. Briefly, an up or down in the chord name immediately after the root affects the 3rd, 6th and/or the 7th, but not the 5th or 9th. Chord progressions are written as Cv7 - vEb^m6 - Fv7 or Iv7 - vbIII^m6 - IVv7.
A fairly exhaustive survey of 41-edo chords is at Kite Guitar Chord Shapes (downmajor tuning).
Here's a printer-friendly chart to get you started, with and without fingerings: