Update on this issue. I replaced the head gasket. I took it out and started mowing. Ran great for about 30 minutes then all the sudden a sputter of the engine and a puff of blue smoke. Continued to do this about every 45 seconds or so. It seemed to be worse if the engine was under more of a load, like running through a patch of thicker grass or going up a hill. It didn't seem to do this at all if the PTO wasn't engaged.
I'm prepared to replace the rings, but obviously that's not a quick or easy job so I just want to be sure there isn't something simple that I'm overlooking that I should check first.
A side note to this discussion, I can understand if the rings are worn and that was causing this issue, but if the rings continuously move A LOT then this wouldn't seem to be an issue of the rings being all aligned, if so, they would soon move to another position and self correct. Either the rings don't move nearly as much as was described earlier, or my problem would not be an issue of ring alignment, in fact, nobody's would. Why would ring gap placement be so important, as we all know it is, if the rings were continuously moving that much?