You’d send the coins to an address owned by yourself. So you lose nothing. It’s impossible to tell that you’re sending the coins to yourself. There’s no need for a “random payment limit” — “laundering” even your entire wallet at once would be harmless.
Choosing random addresses will not be enough, I think. Fiat-to-BitCoin exchangers will always be an “anchor of identity” to a coin, since they know both the identity of the person buying coins and the destination address.