You should give those last two coats of paint a good long while to see if it will get less tacky and "cure".
If it stays tacky I would not try to fix it by trying to plaster an incompatible product like polyurethane on top of the latex paint. This would be an especially big issue if the base paint was not fully cured and dried. In this case the best order ...
washers and longer screws sound like a good solution.
Mixing washers of different types should not be a problem
as they are not going into a wet location.
If the standard washers are not the right thickness shims (thin washers)
can be cut from the side of soft-drink (or beer) cans using scissors.
be careful the cut edges are very sharp.
You've got something better than a schematics, you've got a left side that's working. Take it out of the cabinet and do a forensic study on it. You should be able to put the right side back together. Good luck.
I would probably drill holes through the piping and screw/bolt it directly to the frame. They won't budge if fastened properly with screws. I guess I would glue it as well...
Or how about some straps like these on both sides of each pipe: