Yes, fully agree that the last person doing this repair was not up on the best way.
Signs that somebody has been there before? That pop rivet through the label on front looks very odd and out of place! Screws everywhere but one pop rivet driven through a label?
But that is water under the bridge so you might be looking for the better way to get it done?
That is a good place to look over the interactive parts drawings here:
When getting into it and looking around, you can zoom, tilt, or turn things to get the best view of what they show and the detail is somewhat amazing!
When you turn the valve around to look behind and at what might be better, I can only guess as I have not seen the RV!
But what is right next to that compartment on the right side as viewed from the front?
empty space where you might remove the panel from that side to access that valve without taking all those other fittings off?
View from the back with screws marked?
Drawings may mislead but it "looks" like there is a panel shown in yellow on this snip which has screws to hold it? Maybe look at removing that panel instead of the front where all the handles, ports, etc. clutter the problem?
BUT?
Before going full blown, is there a chance that is a common cutoff valve that might only need a new faucet washer which could be replaced from the front? I might favor taking that center screw out to peek behind, looking for a simple way?
We never know what others may have done before, so I will wish you luck on the project!