I'll add a few things to maybe help the cause, or try to explain it anyway.
We have the newer style Atwood 6 gallon water heater. It has a preset thermostat that mounts on the outside of the tank and is non adjustable.
It is set to shut off at 140F. When the tank cycles down to 115F, it will turn back on. I have never measured those temps but that is what the good book says the T Stat has been preset too.
The 140F can never be used alone as a hot water source to shower with as it will burn you pretty good if you try. This has been talked about a lot on "why so hot?" The answer I was always given was, to make the hot water supply last longer. And in our case it does. We have to blend in cold water to temper it down to not scold you.
We have also put in an Oxygenics shower head (the head, not their stiff hose that comes with it) which uses less water and we installed a single on/off shut off valve in the hose that actually does shut off and not drizzle cold water...
When we started to boondock we had to create ways to be a economizer on everything and not waste so much of, well everything. Water, electricity you name it. On the water side, the combo of the better shower head and the on/off valve in the hose along with a water conserving method allows the wife and I to both a shower back to back without issue. We have never run out of hot water taking 2 showers. We do this all the time.
When we take a shower, we do what is sometimes nicknamed, a Navy shower. You wet yourself, shut off the water. Soap lather up, then rinse if one needs a small area rinsed and shut off the water. Add shampoo as needed, then do a full body rinse and your done.
What I described above works for us and is very comfortable, just you cannot let the water run non stop through your entire showering process.
Now to maybe a few technical things since what Johnnybgood has is different then our system.
He has an "adjustable" T stat, what is it adjusted too? If it is turned down to 110 or 120 max as that is common house hold hot water, then there is very little cold added and the amount of hot water needed will be more to shower with. Understanding 140F can burn you, and you must temper it, does allow to use less hot water.
Next is the mechanical differences. Our T stat is on the outside of the tank. It has it's own set of issues as it has to touch the tank to get a good reading and most times this works OK. On johnnybgoods setup he has an all mechanical system with the gas valve. The exact valve that John has if it is original, I do not think they sell any more, but it can be replaced with an upgraded one. We need to get into model and serial numbers to confirm this but I "believe" this one will replace it. There are a lot of good pics of this this one which is why I'm, linking it. This replaces the White Rogers valve.
Atwood Water Heater 91602 Gas Control Valve Thermostat - Parts & Accessories - RV Water Heaters - RV Appliances
The thermowell on the back of the valve screws into the water heater. That thermowell is directly exposed/submersed in the water. Hard water creates a lot of scale and mineral build up inside water heaters and his may have a good layer of it on the thermowell making getting a good reading not real easy. I myself do not know if up'ing the T stating on the outside will totally overcome the problem as if the probe cannot sense a temp change very fast, it cannot react fast either if it is insulated with high lime/calcium build up.
I do no recall us having a SOC member post on the valve not working right due to high scale issues, of if so, it may not be that common. This might not be John's issues, but just bringing it up as it is technically a possibility.
John, now reading all this, does any of this seem to fit in your case?
Hope this helps