Mules don't make a difference if it's on the same IP.
@OP, I've heard staking is one of the safest way to transfer between accounts - as long as said accounts are of the same level/close to the same level.
In regards to storing GP, it doesn't really matter how you store it - referring to items/cash/bonds etc. It would be beneficial to store it on an often used account that you play legitimately and that has a history of no botting, etc.
I drop trade/trade the money from my main to a mule. Then log off and hop on a VPN with a different Ip and sell the money off the mule. Only been banned once where I lost money, and I have sold ~75-100b.