I like the idea of using tubes to float the back end of the boat, however I am afraid raising the rear is going to add another problem. As the rear is raised, the front tips of the pontoons are going to want to dive into the bank, so you might want to consider putting a couple of old tires under the nose to keep them slightly above the ground. Be a good idea to coat the tires with a layer of grease also as was mentioned. Pushing them as far under the tips of the pontoons is going to be a chore, do the best you can. Also, I would seriously consider tying off the boat to a tractor or bulldozer before starting to inflate the inner tubes. Moving the back end of the boat changes the angle of the pontoons, in the wrong way for what you are trying to do, so support the fronts before starting on raising the back. When raising the back, it will lessen the amount of contact with the ground, and since gravity will take over, the boat will want to go deeper into the water. Whatever you plan to haul the boat out with, have it hooked up before starting to raise the rear of the boat.
Another thing, and something I am not completely familiar with, is using a tube for a flotation device. Seems somewhere I saw a net, that wraps around flotation devices to "contain" the rubber inner tube so that when it was inflated it would not bulge out in places that was not supported and want to "pop". Not sure if this makes sense, and surely doesn't suggest that I think adding a net to contain the tube, but if you happen to have access to old fishing nets, and a little bit of time, might be worth considering. Whatever amount of inner tubes you decide to use under the center deck, have you considered tying two of them together, one on top of the other? Putting them under the deck un-inflated, and then inflating them will give you more height than a single tube, something it seems you need.
Best of luck, keep us posted, and try not to tear up this beautiful boat!
David from jax (who also looked at your location to see if you were in driving distance to come and help!)