How to replace/re-engineer leaking fresh water drains

I'd suggest to use some reinforced hose like you had in parts of the system in lieu of the poly pipe.

If it was me, the whole mess would be scuttled and full-flow ball valves would be the shut off of choice. I'd probably plumb it all with pex, the proper fittings, and crimps, and choose a sharkbite fitting into the tank to ease installation. Any plumbing that needs support would be tied into a stable part of the frame or ancillary support with appropriate pipe hangers.