Another vote for laying the skins flat, or nearly flat, initially at least. I support a large sheet of plywood on hurdles set in a 'V' shape, one side up resting on the tops of the joiny bits, the other resting on the top bar. This allows any liquid to drain off, but not the salt. If you also use hurdles, I discovered the hard way that you need to cover them too, not just the board, as the salt corrodes the metal of the hurdles. Under the edge I put straw to catch the run-off - straw can be burned afterwards.
You can stack your skins about three high, skin to fleece, if you have a lot. I've done 4 high but the top ones slipped every now and then. You do need to keep swapping which ones are on top.
As I mentioned, I usually cover with a sheet of polythene to ward off atmospheric moisture, but it keeps the mice off too. In the depths of winter when it's below zero I don't cover them. I did once see evidence that mice had held a party on the skins - loads of cute footprints in the salt
The other thing which happened was with mole skins, which I layed out in the same way and salted, intending to tan them myself. There were quite a few but the numbers dwindled. Eventually we worked out that we had a rat and it was taking the moleskins back to its den to line the nest. They must have been the comfiest baby rats ever