It's possible to OVER- choke, thereby causing larger or more open patterns rather than tighter ones. Usually, larger pellets (like buckshot) pattern better out of more open chokes, though it is difficult if not impossible to make categorical statements about shotgun patterning. Every shotgun barrel is pretty much a law unto itself and few generalities apply.
A lot depends on your outlook on defensive shotgun patterning also. Some people want the tightest patterns at the longest range they can get, while others prefer open patterns. Apparently you are a tight pattern believer also, but since you didn't say so I hesitate to assume that is the case. Figure out what your longest likely 'engagement distance' is, either inside the house or outside, and use that to establish your own preferred patterning range (distance) and size.
Were I you I'd start with an Improved Cylinder tube, and tighten up by degrees if needed. While it's possible you might wind up using your turkey tube after all, I suspect a more open tube will work better. BUT there's no way to know without trying. Most turkey tubes are extra full, I personally would be reluctant to start out the experiment on buckshot patterns using that tube. Other people are more adventurous than I, however.
My usual 20" RS barrel has a Modified tube. I use Estate 00 for house gun loads also, and I get good even patterns out of the mod tube (it'll keep a complete 9- pellet pattern on a piece of 8X11" typing paper at 25 yards, no stringing and no fliers). This barrel has had its forcing cone extended and was fitted for RemChoke tubes by Colonial Arms, it was originally a Cylinder bore.
Good luck, and Stay Safe.
lpl
