UPDATE: Just wanted to circle back here for anyone else happening upon this post.
Counter to the advice I was given, I ended up taking the gas valve apart, applying my best troubleshooting skills, and then when I didn't find anything obvious, re-assembling it.
I installed it back on the RV and shortly after I lit the pilot light flames sprang forth from all around the valve! Fortunately I was watching and forcefully blew on the flames, which put them out for a second and I was able to shut off the valve. So, obviously I didn't put it back together correctly :-/
So, lesson learned, and @Old-Biscuit was 100% right. I shouldn't have messed with the gas valve and just replaced it - which I did, and it worked perfectly :-)
PS - As it turns out the reason the old valve wasn't working was that it was filling with water. The plastic cover on the temperature probe had been compromised by the threads on the tank and water was leaking in. Photo attached.
