[joe-nwt]

The next time you lose power, measure with a volt meter at the main breaker before you touch anything else. Measure from line to load on each pole. If it's tripped you will read 120V, if it's still closed you should read 0V.

This will tell you if the main breaker has gone bad. Sometimes they trip internally but the handle doesn't move.

 

[joe-nwt]

Go straight to the main breaker in the main panel. Don't touch anything else. Measure where you have indicated. 120V indicates the breaker is open regardless of handle position. 0V indicates the breaker is still closed and the problem might be in the meter base, or more likely the utility connections.

So far I'm guessing the main breaker as the problem goes away on reset.

 

[joe-nwt]

As a really WAG, I'll go with the right hand pole.

 

[joe-nwt]

Correct. But you can check the utility in by measuring line to neutral. Thing is, it's pretty hard to correct a utility problem by resetting a breaker.

 

[joe-nwt]

So does this suggest that the right side of this quad breakers has gone bad?

Well, my WAG paid off! That's exactly what that means.

Yes power will have to be cut to replace that breaker.

The 2.something-ish volts you are reading indicates a high resistance across the contacts. Not high as in kilo ohms or anything but high for contacts. In essence, you were pre-heating the thermal element in that breaker. So when you added a load that should normally not cause a trip, boom, game over.

 

[joe-nwt]

Wait a minute.....there should be no potential between A to B or C to D. Those points are in line....no potential. OP should be reading volts between A to C to get 240v or B to D to get 240v.
He should also test each point to the neutral to get 120v each.

The reading he had of 118esh from C to D might indicate a short downstream on that phase. I think the breaker is doing its job and replacing it will not correct the problem.

I think just maybe he would have noticed a 200A short circuit along the way. A second load in his pants would be his first indication...

 

[joe-nwt]

The lizard didn't get electrocuted from touching the hot leg while sitting on that plastic insulator.

$950 is reasonable for that job in my opinion.

If you lose 1 leg there is absolutely no way you can say what will happen with certainty. The 240volt devices are still connected through the other circuits through a new and strange series/parallel configuration. The results cannot be even guessed at unless you map out every load in the house. So far the load distribution in your panel seems to be in your favour though.