I ran over the meter readings at the receptacle end again just to confirm they were the same as yesterday and they were. Plugged in, start switch, no start no run. So I unplugged the dryer and went out to the breaker box. Checked visually and it hadn't been tripped (no little orange flag in the little window). Switched it off and the switch threw crisp for it's full range of motion, so I don't think it was tripped. Well, it definitely wasn't. Flicked it back on and it felt normal again, so I flicked it back and forth 4 or 5 times just for the hell of it. Left it on, went inside, plugged in dryer, metered the prongs like in the pictures before, and this time I got the 120-120-240 like you had mentioned before. Also while I was metering the big plug, I heard the faintest noise coming from the dryer. I turned over the little dashboard bit where all the controls are mounted and put my ear up against there and could hear the timer clicking. So I pushed the plug the rest of the way in and hit the switch. It started right up. I let it run like a minute with no hickups, and then shut it off. Tried it on several settings, with no problems. Then while it was running I molested the plug at the receptacle in every sort of way (as safely as possible) trying to make it do anything wrong. It never stuttered or shut off like before. I even tried easing the plug out while it was running and wiggling it around as I went and it ran just like normal until the plug was free of the socket.
One thing that concerns me is that during this entire episode from the very beginning a couple of weeks ago, the circuit breaker in the breaker box has never tripped one time. I am now assuming that the breaker is somehow the root of the problem, but I have no experience with anything like that happening before. Is it possible for a household breaker to have a failure mode other than just on/off? I know they are supposed to interrupt current in the case of a spike or short, but how could it be letting some voltage through but not the full flow necessary? I really don't want to go digging into the internals of my breaker box, but I'm guessing I have no choice at this point. Should I just go get a new 30 amp breaker and try to just remove and replace?