I'm not a turkey hunter, so can't comment on the effectiveness of the proposed gun on that particular critter.
I also don't know how shot and wad pressures compare to a patched round ball, or to the .45 caliber MaxiBall, for which your rifle was designed. I think the patent breech on this rifle is inherently stronger than a drum and nipple arrangement, but there will be some limits, one of which may be the diameter of the threaded part of the breech plug.
However, I have a Seneca and do know the Seneca barrel is 13/16" across the flats. You'll not want to go up much in bore size, in any event. I'm thinking you would need to go to at least a 45 gauge (0.470") to eliminate the grooves, but around a 42 gauge (0.481") might be the most to expect, but again, the size of the breech plug may impose a limit. Mr. Hoyt could advise you on this.
For an effective turkey load, you'll need to consider wads, also, and whether or not you can even get them in the size you need.
However, I'm a little uneasy with the whole situation. If you'll permit me to suggest an alternative... Maybe look into getting a T/C Renegade .56 smoothbore. These are not hard to find and you can generally expect to get a good'un for $350 - $450. I got one a few years ago that was (is) in 95% condition or better, off GunBroker or GunsAmerica (I forget), for about $350. In my opinion, T/C should have made these in .55 instead of .56, to make them a true 28 gauge. Not sure how 28 gauge components will fit, probably somewhat loosely, but then again, 010" is not much difference. I haven't tried yet. A lot of guys get these Renegade smoothbores and have them bored out to a larger caliber and rifled. The Renegade barrel is a full inch across the flats.
As it is, the .56 smoothbore will handle round balls or shot. Track of the Wolf carries the recommended .550 balls, if you want to use the gun on bigger game.
The Renegade smoothbore also has more of a shotgun butt, and may point more naturally than your Seneca.
Just my thoughts on the topic. Good luck with your project, and be safe!
Notchy Bob