The cheap flex shafts they sell at Harbor Freight, etc. are useless in my humble opinion. As soon as you put any pressure on the piece they'll want to twist themselves into a knot - not to mention wearing out quickly. The one I use is a good 1-1/2" thick on the outside with a 1/2" threaded shaft on the end, and hooked up to a 1/3 HP electric motor @ 1750 rpm. I have a 1/2" drill chuck that I can thread on there to use smaller tools with it. Caswell sells these:
http://www.caswellplating.com/buffs/indflex_shaft.html - mine is heavier-duty than the one pictured. AS you can see they're fairly expensive.
<<I actually found a sears die-grinder with 6" wheels at a good price but it still won't be able to hit certain sideway spots on the wheels.>>
Are you sure it's a die grinder? I can't imagine using a die grinder with 6" wheels. In fact I don't recommend using anything over 4" in a slow drill or shaft, let alone a grinder.
Having said that the electric drills wear out rapidly, I do have an air drill that works great. Even if you have to stop to let your compressor catch up once in a while, it's a cheap way to go if you already have the compressor.
Fact is, all this is the reason that some of us do polishing professionally. We put the money into getting the right equipment, and the time into learning to use it. And the end result is that our customers do not need to buy the equipment or put in the time learning because we've already done that for them.