If you pull this one off, Fish, it will truly be an epic. One of a kind. Something nobody else has tried.
As for a resupply, you might consider VVR at Edison Lake. They are accessible by snowmobile after a good storm. Road gets dry though, after a few days in the Mono hot springs area. VVR would be a 10-mile r.t. slog, though, from the JMT.
I think I'd want to try later times -- more consolidated snow the later you go. In fresh powder, you might only make a couple of miles in a day!
If you had a sled, some way to strap it on the back of the pack for steep descents might be worth trying.
I agree that water levels would be low. Not much melting going on in that part of the year.
I tried x-c skis, going into the Pear Lake hut in Sequoia. Unless you have lots of experience on them, mastering the telemark turns, they're treacherous on the downhill. They would sure make your up-hill and level travel more pleasant, though. Say.... I can put you in touch with someone here who has done a number of April trans-sierra trips. They always used skis.
