One thing that I forgot to mention, because I didn't think it was important, but when it first did this weirdness, I pulled both side covers off to see if anything obvious was going on and found the rubber oil plug on the left side of the engine had blown out. The plug is old and age hardened and really doesn't fit that tight anymore, so I thought it probably was not related to the issue. I wrapped a thin rag around the portion that fits into the hole and tightened it up.