sticky_beaver, I'm looking at your revised schematic and see you are planning to return bleed air to the engine, after it's been through the cabin.
For me, an old-old engine guy, this presumes that (1) the engine can do something useful with the extra air, and that (2) there's an appropriate place in the engine flowpath to reintroduce this air to the engine cycle. I'm always looking for cycle improvements, and your proposal deserves a fair look.
First of all, the overflow air from the cabin is at about 10-11 psia (equivalent to 8000 ft cabin pressure altitude, approx. - refinement of the numbers welcome!). There's only one place in the engine cycle where this flow could be introduced without backflow - and that's right at the engine fan inlet.
But this reclaimed air is much warmer than the -30C TAT found at cruise, and thus it's of lower density - and the engine would like all the inlet air density it can find, to operate at its best.
Sorry, sticky_beaver, I don't see a practical improvement to the status quo.
