In regard to the playback being better than the LP from the TT; that does seem impossible; the funny thing is, I just enjoyed it without ever thinking about it, but now that this fact is being questioned, I'm forced to think about it.
There have been many threads here about "phono-preamps". The signal from the cartridge; is that the original before it reaches the phono-pre? How many times have you read how tremendously one phono pre improved the sound over another?
On playback, the magnetic signal on the tape is the same as the signal from the cartridge that goes to the phono-preamp , If phono-preamps make such a difference, why not the internal amp in the reel; those amps would make the same difference as phono-preamps.