Alright, I put a new fuse in the scope and hooked-up my DMM to the 140V output taps. Each measured 155.1V. The 35V output taps measured 38V.
When calculating a dropping resistor, I wasn't sure what current value should be used in the equation, so I just used 400mA (the fuse size). At that amperage, and the needed drop being 15.1 volts, an online calculator came up with a 38 Ohm 6 Watt resistor.
I have no idea what the current draw is of this oscilloscope when it's working properly, so would I need to experiment with different values until we find the happy medium? We know what the voltage is now and we know where it needs to be, so here are other values based on different currents:
At 150mA = 101 Ohm 2.26 Watt
At 200mA = 75 Ohm 3.05 Watt
At 250mA = 60 Ohm 3.77 Watt
At 300mA = 50 Ohm 4.53 Watt
At 350mA = 43 Ohm 5.28 Watt
At 400mA = 38 Ohm 6 Watt
Surprisingly, I see plenty of space to bolt a heatsink to the aluminum panel of the chassis.
We need to dump 11% of the voltage somewhere. Do we need a chimney