Current Mirror Controlled Switch
I have modelled it in LTSpice below using a resistor for the load but the IR6 doesn't match the IR7. Even without the load the IR7 is still not equal to IR6.

In an inverse current mirror, it's assumed that the transistors are matched and emitters are shorted:



simulate this circuit &ndash; Schematic created using CircuitLab
But, in the OP's circuit, it's almost impossible to match the collector currents because \$\mathrm{V_{BE-Q1} = V_{DS-M1} + V_{BE-Q2}}\$. And, as you might already know, \$\mathrm{V_{DS-M1}}\$ is proportional to load current: \$\mathrm{V_{DS-M1} = R_{DS}\cdot I_L}\$. I don't know if the MOSFET is fully modeled in the simulator, but from the datasheet, it can be seen that \$\mathrm{R_{DS-on}\approx25m\Omega}\$ for \$\mathrm{I_{LOAD}=1A}\$ and \$\mathrm{V_{GS}=-4.5V}\$. This means that the drop across the M1 will be around 25 mV. So the difference of \$\mathrm{V_{BE}}\$ between Q1 and Q2 will be 25mV, theoretically.

How do I derive VG for a given load?

Since the Q1-Q2 pair does not form a real inverse current mirror, \$\mathrm{I_{C-Q2}}\$ will not be completely dependent on the R6 (or in other words, Q1's collector current). Instead, it'll be more dependent on \$\mathrm{V_{BE-Q2}}\$ and the load current.



simulate this circuit
I couldn't really derive Vg but I can say that the idea is to keep Q2 off when VS is positive and greater than VO, and the load current is non-zero. Q2's crucial role is to force M1 off when the voltage is applied from VO-side instead of VS-side. So it may not be needed to be turned on during the normal operation.
When M1 is on, since the load current flows through RDS of M1, there'll be a drop across M1. The higher the load current, the higher the drop across M1, and finally the more the Q2 reaches turn-off (because VBE approaches more to zero). The lower the load current, the more likely the VBE of Q2 to be equal to that of Q1. This leads the Q2 to turn on more and make R2's upper-end voltage nearly VO. So M1 will turn off because its VGS becomes zero.