Rory, first of all, congratulations for your arrangement!
Now, to answer your question, I think that the rhytm part sounds very authentic; the only thing missing are some fills here and there, but that's not a big problem. The second thing I loved was your piano solo (nice reference to "Eleanor Rigby", btw), while the third thing was of course your sax solo. Speaking of the sax, I think that it has a different reverberation compared with the piano and the percussions and sounds like it's in another room; this is the only element that could make one think to a prerecorded sequence. Other than that, the "live" feel is really astonishing and I could swear that I am listening to real musicians playing at the same time.
Once again, congratulations for your talent as a multi-instrumentalist!