Determine voltage drop over 10G resistors with cheap multimeter

Do what the ancients did ==== use a Wheatstone bridge. Like this

^{simulate this circuit – Schematic created using CircuitLab}

Rotate the 10,000 ohm potentiometer for ZERO reading.

Then measure the pot voltage (and compensate for the DVM loading)

sure, a voltage follower built with a FET op-amp that has extremely low input bias current.

https://www.mouser.co.uk/Semiconductors/Amplifier-ICs/Operational-Amplifiers-Op-Amps/_/N-4h00g?Rl=4h00gZgjdhpmZ1yvbz5oZ1yve6dbSGT