Anything from a TG SSX to a 570 of a lot of different makes can work. A 560-570 will normally get you there without over choking it and provide a nice pattern for turkey killing. These super tight really high pellet count chokes generally require optics and have been the cause of a lot of misses along with the many kills reported. The 20 gauge is much less forgiving of what chokes work than the 12 gauge. They just seem to have a different personality about them.
Whether you meant H-13 #7s or Fed HW #7s, a non-ported choke does well in general with both.
This is most likely an invector thread on your gun.