Interesting concept. How do you avoid reingesting exhaust gases, both leakage between stages and at the air inlet. I assume exhaust gas does another 180 and goes through the fan?
Turbine stage count is usually much lower than compressor stage count. How is this handled?
VSVs look like they would be impractical as the operating mechanisms would be in or through the exhaust ducts.
For VTOL applications I assume you want as high a bypass ratio as possible (due to low speed operation).
If you chose a DEP route instead of turbofan, I wonder whether you could bury the motor-generator(s) inside the compressor as well.