Well dang Beenthere, ya saved me a lot of typing. The technique you described is one of my favorites, on machines that can be jacked up.
For machines that can't be jacked up, I lay em out on the floor, drive over the chain, and attach one end of the chain to the tire with a bunji or rope and back the chain onto the tire. This works pretty well especially if you have a helper to keep the chain taught. When you get the chain about 2/3 on the tire, stop the machine and link the chain up. Move the machine back & forth to get the slack out, retighten the side chains, and go to work. Usually, after a mile or so, you can pull the rest of the slack out of the side chains.