OK, here are more data:
Refinery efficiency: The paper I cited said 88%.
Everything else: From https://en.wikipedia.org/wiki/Energy_conversion_efficiency, I use the mid point numbers from Wiki for computation.
Gas efficiency: gas motor ~.3%, refinery ~88% net: 0.3 * 0.88 = 0.264
EV efficiency: Li battery ~85%, Motor ~ 70%, power plant ~30% (Wiki said up to 40%), net: 0.85 * 0.7 * 0.3 = 0.179
Gas is 47% more energy efficient (.26/.18=1.46). If you don't use solar/wind..., EV generate more green house gas, by 47%
Gas turbine Chemical to electrical up to 40%
Gas turbine plus steam turbine(combined cycle) Chemical/thermal to electrical up to 60%
Lithium-ion battery Chemical to electrical/reversible 80–90% [9]
Electric motor Electrical to kinetic 70–99.99% (> 200 W); 50–90% (10–200 W); 30–60% (< 10 W)
Combustion engine Chemical to kinetic 10–50%[12]
I see you penalized the electric motor efficiency but took the 88% refinery as the low end.
So,
EV efficiency: Li battery ~85%, Motor ~ 80%, power plant ~50% (Wiki said up to 60%), net: 0.85 * 0.8 * 0.5 = 0.34
Electric is 31% more energy efficient (.34/.26=1.31). If you don't use solar/wind..., EV generate less green house gas, by 31%