I was trying to push a 3" length of mesquite through the band saw with a board. Circumference PARALLEL to the blade. Sure enough, it got spinning and took off! I still haven't found it.
The final straw was trying to cut the 1/2" piece off the mesquite. I wish I'd gotten to the switch earlier, but it wasn't worth getting in front of a potential kickback that DID become a kickback. That prompted my post.
Just to take a moment to return to the bandsaw part of this discussion...you were on the right track, imho, by trying to do this cut on the bandsaw rather than the tablesaw. As you learned, free-handing a cross-cut on a circular workpiece on the bandsaw will literally get out of hand in a heartbeat. However, there are a couple of ways to make this cut safely...1) use the miter gage and clamp the round piece firmly to the face of the gauge...you might have to put an extension on the gauge. Or, 2) make a V-shaped block, like a cradle for the workpiece and either clamp the piece to the cradle or use the miter gage to push workpiece and cradle together through the bandsaw blade. Either method is safer than using the table saw for this kind of cut. I have used method 1) to cross-cut irregular limbs up to about 4 inches in diameter.
As far as not getting to the switch in time to prevent a kickback of a small cut-off trapped inside the upper guard, you might consider adding a foot switch to the system. Shopsmith sells one and it is well worth having. It comes in handy often when making table saw cuts that leave you far from the headstock switch at the end of the cut, and also for routing with the speed increaser.
And, as others have said, read Power Tool Woodworking for Everyone, and any book you can find by Nick Engler.