The key is you do not want any water to get in the first stage. If you simply submerge everything, water can get into the LP hoses thru Atomic's unsealed orifice in the 2nd stages. If this happens, it can travel thru the hoses and into the 1st stage where it mayl cause corrosion. With that in mind, I can think of a few options. Use two soaking tubs; one for the 1st stage and one for the 2nds. Keeping the hoses as the high point will keep water from traveling into the 1st. Then make sure you dry & store it with the 1st stage higher than the 2nds so water can't flow into the 1st. Or, disassemble the LP hoses from the 1st and plug the ports. Soak everything, blow out and dry the LP hoses good before you reassemble.
Best solution is buy a tank. Shop around at area LDSs for a used one. You can then go diving without having to deal with tank pickup and drop off, and your reg care can be done properly.