Tough situation. I think your best bet would be to buy your own camp. You can keep all the luggage in jeep/SUV and enjoy a sound sleep in camp. 3 person (4 can also accommodate if no luggage in camp) higher camp can be purchased for 7.5k
Other option is to rent the wildlife guard tents. They have five tents setup (just saw in picture from last year trip) and each tent can accommodate 7 to 10 people. So its bright chance that you will get one for rent at the spot.
If you rent a camp from Astore, ask them and they might have another office/representative in Skardu to whom you can handover the equipments after Deosai.