Due to upper-back issues I only dive single tank back mount and use a backplate and wing.
To store I inflate my wing and hang in my garage where I have clothes rack with with wire shelves on one side.
I connect the rear D-ring of my crotch strap to a carabiner connected to the rack so that the corrugated hose is the lowest point. This allows any residual water to drain towards/into the hose and I hit the purge button on the inflator to release any water that has collected. I orally inflate fully and repeat until no water comes out.
I then orally re-inflate the wing roughly 80-90% full and leave the rig hanging until next use.
I don't inflate fully because if my rack was to fall over, the fully inflated wing may be more prone to damage should anything land on it.
I have been storing my wing like this since I starting diving a bp/w and have not noticed any issues caused by it.
Here is an image of the rack I have:
I have loops of paracord girth hitched around the top front and back cross-members with large carabiners clipped to them, Our BP/Ws and BCDs hang from them (2 on the front and 2 on the back).
Spools/reel, DSMBs, computers, compasses, torches get clipped to the underside of the top rack on the left side using the boltsnaps tied to the device, double-enders , or smaller keychain type carabiners (computers/compasses in bungee mounts).
Fins are stored hanging from the plastic cross-members on the right side...adjustable heel straps are clipped around the plastic side pieces, and I drilled holes to slot "S" hooks to hang fins with bungeee heel straps from. Reg sets are coiled and suspended by paracord loops clipped to small carabiners slung on the plastic cross-members on the left side. I do not have the bar across the middle installed.
On the shelves I have plastic bins similar to this to store masks, gloves, hoods, and booties.
-Z