I agree with you about not "tinkering" with what works. After years of testing turkey chokes, I've found that price does not always dictate quality or performance.
One excellent choice for the SBE II is the Wright's Turkey Choke. It's a limited production item but is an excellent choke. It has a long parallel section and comes with 3 different parallel sections. The #1 is .670 and is great with the Federal Flitecontrol Wad Shells. The #2 is .660 and is the most "forgiving" of the chokes on the market. You can use a variety of shells and get good performance with it. The #3 is .650 and is best with the Winchester HV shells, the Winchester XRHD shells and the Remington Wingmaster HD shells, all with #6 shot.
You can see those chokes at http://www.allaboutshooting.com