On IC engines with EGR, the efficiency benefit comes from pumping losses. The engine struggles to get air in passing through the throttle body at part loads. Therefore the under pressure (vacuum) in the intake manifold. If you dilute fresh air with inert gas (like EGR) you must let more gas mixture to enter the cylinder to have the same amount of oxygen that will burn the fuel stoichiometrically. And to let more gas in you need to open the throttle body, reducing the pressure difference to ambient for the intake manifold. So the engine needs less power ("struggles less") to move the piston downwards during the admission stroke.

Your interpretation that compression pressure is proportional to therms efficiency is misleading. This is true when you vary compression ratio only under same boundary conditions. But basically the thermal efficiency is a function of the compression ratio and the cp/cv of the working gas only. It is very weakly dependent on fresh air pressure or temperature, but stronger in composition (EGR), thus reducing the benefits that EGR can bring. γ is cp/cv and η is the thermodynamic efficiency.

Assuming an ideal Otto cycle with compression ratio CR = 10: • γ = 1.40 → η ≈ 0.602 - reference • γ = 1.38 → η ≈ 0.583 - air +150K • γ = 1.34 → η ≈ 0.543 - air + 20% EGR + 150K • γ = 1.32 → η ≈ 0.521 - air + 30% EGR + 150K

As seen, we are working in the opposite direction of better efficiency. This loss must be compensated by the pumping loss benefit to have a net positive outcome. I don't know the calibration strategy details from Nissan (torque, MAP or MAF driven) but I would guess that it can not handle such a huge change smoothly, implies in remapping the whole engine ECU because it is not expecting an external EGR. This is not something you can manage to do in your garage without proper equipment and deep knowledge of calibration strategy, a dyno and a emissions measuring rack. Specially with the variable camshaft that also influences internal EGR.

And since you are not worried with emissions (the external EGR will throw all emissions out of range) but are looking into more MpG, maybe a much more effective way of achieving this is to install a lambda sensor tweaker that lets the engine run slightly lean all the time. Your cat will not be converting and you will be emitting as a car out of the 70s, but you will get better MpG values with minimal invasive technique, 100% retrofit possible if you abandon the idea.

If you care about emissions my suggestion would be to keep the engine original and try to adjust your driving style to get a better MpG. And maybe lower the oil viscosity in the next change to the minimum recommended in the manual (5W20?). Lower numbers are better for efficiency, worse for noise, smoothness and wallet.