Thought about this for a while:
I don't know your skill level, but if you're ok with 40 degree hard snow and have a few days to play around on Rainier to get used to the altitude you might try this - hike in to the Turtle, (9,400')and camp there. The next day climb the Finger to the top of Wapowety Cleaver (11,800?') and descend the Kautz back to camp. Next day climb the Wilson Headwall to the same destination and back down the Kautz. Third day climb the Kautz all the way to the summit. You will have done three "routes" that are reasonably different from each other, camped low enough to be comfortable/enjoyable/protected, and had enough time/altitude to be prepped for the summit with a light(er) pack.
Condition your evaluation of such advice by the fact that I've never heard of anyone actually doing it this way. However, my experience on all three routes would lead me to believe that it would work and you would enjoy it and accomplish your goals.
What do others think?
BDS