Hint 1
Label the canisters left to right 1 through 7, then turn them in this order, sliding the rack to bring the canister you're turning to the circular position where canister 7 is when you start:
7-5-7-6-7 3-7-6-7-5 7-6-7-4-7 6-7-5-7-6 7-1-7-6-7 5-7-6-7-4 7-6-7-5-7 6-7-3-7-6 7-5-7-6-7 4-7-6-7-5 7-6-7-2-7 6-7-5-7-6 7-4-7-6-7 5-7-6-7-3 7-6-7-5-7 6-7-4-7-6 7-5-7-6-7
Now grab the whole rack and whiz them to the far right -- then save your game, because you do NOT want to have to do this again.
