Not really related to mixing, but why are you using multisig addresses for your hot wallet? Seems like a waste of fees (371 bytes for 1 input and 2 outputs) compared to segwit (140 bytes for 1 input and 2 outputs), which is what I thought you were using or traditional addresses. You could save 3 times the fees, and I don't think multisig really helps in this case.
Also, if you don't log, how does a unique code help? Wouldn't you need to at least store the group the coins were in, which means you do log?
We using multisig for security reasons (for what it was created), i cant explain how our service work with it, but it can help in some cases with save coins. We know that fees are higher for multisig, but security is more important.
As you sent coins to input address we mark it with "code", that's only what we have about your transaction after invalidation (deleting order). When you create new order with same code we will send you money except addresses which are marked with this code, it will avoid the fact that in future you can receive a part of funds you sent to our service before. Bitmixer worked the same. Of course we have our base encrypted, tor server separated from public clearnet proxy and so on.