I also have a strange affinity for the pressure fed system but have had similar problems. It is the ONLY thing I don't have working after my resto. I replaced all the hoses, but I cannot find a hose that can hold the pressure between the spare tire and the bottle. Try spraying all of the fittings from your spare tire to the bottle with soapy water and see if any of yours are seeping air. Mine were slowly seeping so after about 3 days, my spare tire was flat. Note that the check valve to keep the tire from going flat is in the cap for the bottle, so any leakage before the cap will result in a flat tire. I've had no problems with leaks downstream of the water bottle; only the run from the tire to bottle. That's probably because downstream of the bottle is filled with liquid that seals better.
My main leak was the screw-on fitting to the schrader valve on the tire. I replaced that with
this one from amazon. That fixed the main leak but air was still slowly seeping around the hoses at all fittings. The hose I bought is supposed to heat set by soaking in hot water before installing. I even tried boiling water, but the hose is just too soft to hold 42 psi. The factory installed rubber bands at the fittings to reinforce them, but they are NLA. I tried heat shrink instead, but no luck. I also bought a length of OEM hose from Volkswagen but instead of the 2m length in the product description, it came as a short 2 ft. piece that was worthless to me. That's when I got frustrated and set the project aside.
I'd like to find the proper hose that fits tight on the fittings and can withstand the pressure, but so far have had no luck.
There is a website that lists some sources, but they are out of date and I haven't been able to source the same hose. I guess the other option is to figure out some kind of clamp to squeeze the hose tight to the barb fittings. Simple twisted wire might work, but would look like
I don't think this helps you any, but that's where I am in my quest to get the quirky washer mechanism functioning again.