But I digress, the question was is that kind of pool technically feasible to implement (or am I barking mad because that is what P2Pool is)?
This:
Just wondering, can we not have the best of both worlds by solo-mining AND submiting to a pool at the same time?
Is not possible to implement, as the puzzle you are solving includes the definition of who gets paid.
You can either solve a problem that involves paying yourself all of the block reward, or you can solve a problem that involves paying the pool the block reward.
It is impossible to solve both problems simultaneously.