Okay, this assumes that you are getting the flexane cheap because it isn't really cheap stuff, and judging from the pictures, I don't think you want to put a whole lot of money into this boat, correct?
Okay, I did not get rid of the older patch material on my raft, and I don't think I would recommend getting rid of it. It goes over very nicely, and adds another layer of protection. It seems to help hold patch jobs in place, but I wouldn't want to bet on it being very good patch material by itself, if that makes sense.
You should have no problem with the flaxane sticking to the bottom of your raft. It is like tar, and I doubt there is anything it won't attach to. It would be interesting to put it on a CPVC pipe to see how it does. I'd bet it would stick to that, even. I forget my original thread and precisely how I prepared the bottom, but I think it was just cleaner (I used rubbing alcohol), light sanding to rough it up (and I don't know that it really needed it, but I am use to doing it when I do a patch), and then alcohol again to get the sanding dust off. That's it, and it will stick like mad.
Keep in mind that on mine, I did the entire underside because it was an inflatable floor, and I had hundreds of pinhole leaks that were a constant problem This cured it, and while the rest of the boat ended up dying on me, the floor was amazing. BUT, when I did my bucket boat, I only went along the areas that were worn, and the areas where there had been long patches. If I were doing your boat, I wouldn't do the entire underside. Not becuase it won't work, but because you probably don't need that. I went all the way down the tube because the wear pad was pretty darn worn. But everywhere else, I just went across, sealed over some problem areas, reinforced at the first thrwart, where I seemed to get leaks from my cooler barging into the rocks, etc. That said, I have never had any water get trapped from the top by getting into areas. The flexane will not give pockets for water to be trapped, and the top should be patched in a traditional fashion if you have any large "flaps" around.
That's all I can do for you. I haven't had to replace a valve or put a floor down....yet.
The bottom right picture of the red rubber desintegrating. That would be an excellent test of the flexane. Sand away all the lose stuff, and spread it on, and I'll bet it does wonders. Good luck.