Bill McCartney,
Ported choke tubes don't help in reducing recoil as much as most folks think they do. You'd be better served by purchasing a mercury recoil reducer. They're also very loud!
Talk with some of the guys on
www.waterfowler.com about ported and non-ported choke tubes and you'll read some interesting posts.
Non-ported and extended choke tubes (generally) give the best patterns.
As for Hevi-Shot....you'd have to use a lot less restriction than you would in a standard turkey choke tube. A modified choke might produce extra full patterns, in some shotguns. I don't have any personal experience with Hevi-Shot.
I use a Hastings .665 extended non-ported choke tube for my Benelli Nova with lead shot and obtain excellent patterns. Briley works well with Benelli shotguns too and are as affordable as Hastings.
I hope this info was of some help to you.
Good hunting, Bowhunter57