If the engine is running the MOST efficient way of running the A/C pretty much has to be directly off the ICE. Its a simple matter of energy (all power comes from the engine--none of it is free, even the regen is recaptured ICE drive energy that would have been burned up heating the brake pads).... it will be more efficient to pump the compressor directly rather than turn a generator, make electricity, store it in a battery, turn another electric motor to pump a compressor... there are losses all along that path. The hybrid systems efficiency comes from no idles, recaptured braking energy, and load balancing when the ICE is on....

If you have alot of different loads and speeds on the compressor then presumably you'd need differing RPM and torques to turn it at the best output. The FEH plays that balance in its transmission by balancing high torque low RPM electric effiency against high RPM lower torque ICE efficiency... the transmission makes those decisions for driving the wheels all the time.... but you aren't going to build such a system from scratch for your A/C.

I think hooking up ones own electric A/C in some homemade way might end up making one more comfy... but I doubt its going to do anything for your gas mileage.