Would it help if you restructured that way payments were sent so that it wouldn't always be new coins from the change of the last transaction? Like maybe break your stash into a bunch of .05 addresses and let them age and then you can send them out with no change?
No. The only way to "break your stash" is to create transactions that are broadcast; splitting your wallet into lots of small transactions makes the problem worse for you and everybody else (it is more 'expensive' to handle fistfulls of nickels and pennies, even in the bitcoin world).