Agile- Unless I misread your post, the AE440 diesel engine seems to be exactly that. In fact, with regards to your KW/L metric the AE440 displaces 4.6L and produces 322KW, which works out to almost 70KW/L.
Heck, the AE440 diesel even uses a pair of single stage centrifugal air compressors, each one coupled to its own single stage radial inflow gas turbine. They just call them turbochargers.
If you listen closely when the engine is operating under load, you can probably still hear some of that "sweet turbine whine".
One other very nice thing about a recip turbodiesel that I do not recall hearing mentioned is that it does not have a susceptibility to damage from debris/dust/sand ingestion that a turbine engine does. Perfect for operating in desert environments.