That seems troublesome to build. Only the 10x 1G resistors need to be in oil or potted. It would probably be a lot more convenient to get axial resistors and assemble them into a thick walled Perspex tube that can be used as the EHT probe and fill it with melted petroleum jelly. Perspex is OK up to 90°C for short-term use, so you can use a hair-drier or hot air gun on low to keep the jelly melted while you tap out all air bubbles. Why petroleum jelly, not oil? Well its a decent dielectric, and if the seals aren't perfect it wont leak so readily as oil if you can keep it below its melting point, yet its still very easy to clean off the resistors if you ever need to do any maintenance. The tube ends could be plugged with neutral cure silicone sealant, but my preference would be brass plugs with double O ring seals.
Although screening the 10G resistor assembly is desirable it severely increases the dielectric stress on the perspex tube, and you would need 100KV insulation over the screen at the 'hot' end. Also the effect of the distributed capacitance to ground from the resistor chain to the screen would be to over-voltage the first few resistors during fast transients e.g if the EHT source sparks to the probe or to ground.
Direct readout on a DMM on a 2V range should be possible - its input impedance will be high compared to the 100K lower resistor in the divider. Put a good quality 0.1uF capacitor across the 100K resistor to swamp the stray capacitance across the resistors in the divider chain. Use a NE2 neon bulb in parallel to protect the DMM if the 10G resistor chain breaks down or flashes over
Caution: if the ground lead comes off, it will blow the DMM.