Ed,
Depending on the effect you're after, you might try the 'wedge' method. Technically they are compound segments rather than staves. A stave is typically ripped from a board and a compound segment is crosscut from a board, but they can both achieve the same appearance.
The traditional method of cutting staves is to tilt the blade and set the miter at non-standard angles. It is difficult to get these angles set correctly and errors of 1/10th degrees is problematic. This is where the wedge method can be helpful.
If you want to add a compound segment ring where the slope is 40 degrees (for example), take a turning square of scrap wood that is 2.5" x 2.5" x 18" (or so) and tilt the table of your bandsaw to 40 degrees and cut the block lengthwise. You'll now have a wedge-shaped 18" length of wood that has three angles - 90 degrees, 40 degrees and 50 degrees. Use double sided tape to adhere this wedge to your miter fence. When you now lay your board on this wedge, it is already in its intended slope which means that you can now leave your saw blade perpendicular to the table top and set the miter at the standard number of degrees (15 degrees for 12 segments).
Before I do this, though, I take the board I'm going to use and rip the two long edges at the angle of 90 degrees minus your desired slope (90 - 40 = 50 degrees). I usually do this at the bandsaw. Once you have done this, you should be able to look at the end of the board and see a parallelogram. If you do this before cutting the segments, the ring made from them will already have a flat top and bottom and requires just a little effort to completely flatten it so that it can be added to the vessel.
The beauty of this approach is that a single wedge can be used for either a 40 or 50 degree slope or a 30 or 60 degree slope. I have three different wedges hanging on my wall and use them whenever possible.
Obviously, this won't work if the height of the ring is more than can be cut with your blade fully extended.
This process basically duplicates the process of cutting crown molding on a miter saw where the molding is tipped into its intended slope so that presets can be used to set the miter and tilting the blade is not required.
Lloyd