That gun sounds like a real treasure and I can certainly understand your wanting to try it for turkeys. My first turkey gun had a fixed full choke. A 25 yard shot was a long shot and as far as any ethical turkey hunter considered. No one actually patterned guns back then. Several years ago I took that same gun to the range and was horrified to see how poorly it patterned.
My major concern with your heirloom would be the steel in the barrel. In the 1940s when your gun would have been made, if my math is correct, the steel used was much softer than what is used today. A gun that began with a full choke, if it was shot a lot, could easily be turned into modified choke due to the expansion of the muzzle. Modern shells with tungsten shot or even shot encased in resin, could damage your bore.
If I were to shoot that gun, I'd look at something like Classic Doubles
https://www.hevishot.com/catalog/classic-doubles/ or some low brass 20 gauge shells. I would not do any of that however until I had a competent gunsmith check the gun over and make sure it was safe for modern ammo.
Whatever you decide, you have a gun that has a lot of history and I'm glad you have it.
Thanks,
Clark