After my experience with over adjusting the rear brake and heating up the drum, I was advised and ultimately decided to purchase a cycle jack. This will let me get the rear wheel off the ground when I need to., and there are also other uses for this jack, especially at this price.
The Sears Craftsman Jack has gotten good reviews, and there is a Sears Hardware store a couple of miles from my house. I called them to see if they had them in stock, they did, and I went over last night and bought one.
They are on sale right now for $69, so with sales tax, I walked out with the new jack for $75.