211218-1446 EST
I have now reread the first post, and several others. Really there is not much need to look at what happens at the dryer other than it is a convenient location to measure current. The problem is not at the dryer.
The dryer is fed directly from the main panel, and there is no mention that any of the other devices that show a voltage variation are on this same breaker.
Therefore, with the given information the problem is certainly not with the dryer or its own circuit.
The problem is somewhere that is common to the dryer, and the other circuits.
Some other considerations ---
There is enough information to indicate that the motor is 120 V, not 240.
What kind of instrumentation, and in what mode, is being used that you can see a 50 A pulse on the instrument?
Only a meter such as a Floke 87 in 1 millisec mode would produce a 50 A reading if the pulse width was short as is expected. On my dryer I can not get a 50 A reading until I use the 1 mS mode. A long duration starting current implies very low supply voltage. I am now inclined to guess that you have a high resistance in the very input part of your main panel, or a power company problem.
So a voltage measurement of each input phase on the input wires relative to neutral during dryer startup using both the meter and 15 W bulbs is needed.
If both phases drop in voltage at dryer startup, then the problem is in the power company transformer, or before it.
If one voltage drops, and the other rises, then it is a neutral problem.
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