From the Dino permit brochure: See the "Other Inflatable Crafts". It looks like 3 chambers would work - Your 2 tubes and the floor make 3.
Watercraft Types and Quantity
Inflatable Rafts and Dories
If used on a private trip, the names of commercial river running companies on
watercraft must be covered for the duration of the trip.
Cataraft boats and inflatable rafts must have at least four separate chambers. Solo
2-chambered crafts are prohibited.
Rafts longer than 19 feet without frame and oars are prohibited.
Drift boats without secure, appropriate flotation or sealed chambers are prohibited.
Tying in some air mattresses does not meet this requirement.
Other Inflatable Crafts
Inflatable kayaks, packrafts, ‘shredders,’ paddlecats, ‘mini-mes,’or ‘stingers,’ with
three separate air chambers, designed for whitewater use, are approved for use in
the Monument. Craft must be made from robust materials like Hypalon, Urethane,
Neoprene, or PVC.