I have used Flex Hones for a lot of barrel cleanup, but not chambers. They can be more aggressive than people think in the large grit sizes. I will say that slow and oil are good but I think the most important thing is to keep them moving fast. A slow drive speed will avoid waves but rapid movement in and out is more important in my mind. I have found that the final polish requires more drive speed in order to get a slick polish.
One thing you might try is to run a bore gauge through the chamber and forcing cone. Personally I would doubt that a forcing cone would lead to sticking shells, even if the chamber is shorter than the cartridge. There may be a bulge in the chamber due to bad alignment of the chamber reamer, but the most likely areas are a tight rim or a tight chamber at the base. Try a few different shell brands, inspect the fit of the rims and the look of the fired hulls. The fit of the ejector/extractor may be the culprit.
I have solved more problems like this with a hand turned chamber reamer than with a hone.