well that sucks that is happening with all that extra effort. I see where you are coming from with the cleanliness of what's already there.
Any kind of possibility to access the supply plumbing elsewhere in the house such as the crawlspace or a different room that you are willing to cut out some drywall?
A few years back at my parents house 2 of the bathrooms sit ontop of eachother on different floors. We completely re-did the upstairs with mostly tile and had a loud valve issue with slight hammer with a very nice sink we installed. Our solution was to gain access to the plumbing in the plumbing down in the bathroom below as that was going to be the next remodel
good luck with that