When I "kill" the V0 source, it becomes a wire and the voltage across the gap is the voltage across the network containing R2, R3 and R4.
I'm having a hard time understanding why that's the case.
If you drew the circuit after "killing" the Vo voltage source, you would get this equivalent circuit:
simulate this circuit – Schematic created using CircuitLab
If then you applied the series and parallel transformation of the R2, R3 and R4 network, you'd get:
simulate this circuit
In this form, it is perhaps more obvious that the voltage across the gap (a-b) is the voltage across the resistor network, which can be solved using Ohm's Law.
Do bear in mind that the result is only the consequence of shutting down the Vo voltage source and hence is only due to the current source creating a voltage drop across resistors. You will have to account for the Vo's contribution to find out the voltage across the gap.