Being a newbie, my advise may be taken with a grain of salt, but here goes. When you first demonstrated the LeCroy in the first tear down and powered the unit, you blew your circuit breaker. Upon reset of the breaker, you were able to power the oscilloscope and it appeared to operate albeit with several obvious glitches--errors on the DACs, inaccurate readings, dodgy signal traces, etc. Also, when you showed us the interior of the power supply, it looked pretty crusty and full of all kinds of potentially faulty capacitors.
To my knowledge, 3.3V CPUs are notorious current hogs. Even today's multiprocessor CPU can draw 90 to 125 Watts of power. For 90W @ 3.3V that's approx 27 1/4 amps. Although, the processors in the scope don't come close to the component capacity in today's CPUs, you still have 4 processors powered by the 3.3V rail. So, a 11.2A to 10.2A draw from the 3.3V rail seems a plausible power draw for this circuitry.
Therefore, like several of those who posted before me, I think there is strong possibility that the 3.3V rail in the power supply requires closer inspection. A major portion of the scope's functions is dependent on the components powered by the 3.3V rail. If this power rail is faulty, it could explain most, if not all, of the errors including the breaker tripping, demonstrated in the first video.