Water Heaters - Pilot Goes Out After Water Gets Hot

My AO Smith water heater is only 11 months old. Its been working fine until this week, when one morning the hot water ran out. When I checked, the pilot light had gone off. It re-lit fine, but the next morning the hot water again didn't last through two showers. I checked and again the pilot light was out. So, I replaced the thermocouple. Next morning, same problem!

So, I fiddled with it...and found that after re-lighting the pilot light, the burner would come on (because the water was now cool). If I turned the knob back to "pilot" the burner would go out, but the pilot would stay lit. I did this several times, it all seemed good.

Then, I re-lit the pilot, turned it to "on" and the burner came on fine. But when I turned the thermostat down to the "warm" setting and heard it click, the pilot light went out!

I conducted this experiment several times, and have tentatively concluded that it is the thermostat that is bad and will require replacing. Does this sound right?

How does one go about replacing the thermostat? I see there are some inaccessible screws on the back of it, that can't be got to without unscrewing the whole thermostat and the short pipe it's mounted on from the tank. So, are these the correct steps:

1. turn off the gas stop-****
2. disconnect the gas supply
3. disconnect the thermocouple, starter switch, dead-switch, gas-burner-tube and pilot tube
4. find a super big wrench and
5. apply wrench directly to the thermostat, turning in a counter-clockwise direction

Thanks for any pointers!
Oh, it's a Whilrpool model BFG1J505J13N0V product no. 0733146.

there are some brands that mostly have that no proof from the pilot or going out situation.you might want to google that brand to see if there is a recall on the gas valve itself causing the problem.if you were to remove the gas valve you want to slip a wrench in between the tank and get on the valve square .... give it a short CCW push to break it loose out of the tank fitting.

It's only 11 months old? Warranty work I would think. Is there a reason you don't just call them?