… later…
When you said you had played “rubato”, I had (mis)understood that you had played “freely” (i.e. ignoring Cubase’s metronome completely), whereas in fact (from what I see in your .cpr, but please correct me if I’ve gotten it wrong again 
) ), you seem to have recorded at a steady 110 BPM (not 100 BPM as you wrote earlier), or at least, after quantizing, the recorded MIDI does line up perfectly with Cubase’s grid, when Cubase’s tempo is set to a fixed 110 BPM (well, at least, after having dragged the events, so that the Piano starts on the first beat of bar #2 here).
Am I now right in thinking that, after quantizing, and before doing any tapping at all, the music was already in perfect sync with Cubase’s grid/metronome? If so, then no tapping is necessary. But as you said, after quantizing, the result is very mechanical. (and in this case, the most direct approach is to set everything to Musical Timebase, then edit the tempo track… or use the Tempo Track Editor’s Tempo Recording slider… although it is a little difficult to control the results).
Or… different approach 
…
Were you happy with the (rubato) tempo of your recording, before quantizing (but you wanted to get Cubase’s grid to line up with it, so that the other tracks could be in sync/edited)?
If so, the method I had described was in fact correct, but you shouldn’t have quantized your playing…
The whole purpose of “Merge Tempo from Tapping” is to allow to get Cubase’s grid (and therefore, metronome) to line up with already-recorded music, without changing the way the music sounds at all (in other words the notes stay, physically, in exactly the same place in time, while the grid is adjusted to fit it, rather than the other way round)
Also, I had meant that your tapping should match the music that you were actually hearing (i.e. it should have been like any other overdub)… looking at your new tempo track here (btw, the MIDI events on your tapping track are missing, except for the first three bars), I can only guess that what you were tapping never matched the music at all… were you, instead, tapping out what you wanted the tempo to eventually be? (I’m afraid Cubase isn’t capable of that function, it would require to slave to MIDI Clock, and Cubase doesn’t have that).
(I also observe, from your tempo track, that there are tempo events only every half-note, not quarter note, which would partly explain why the end result was incorrect).
So, have I managed to confuse you still further? 
(if so, just erase your memory of the last few days completely from your brain! )
To recap… apart from getting the music and the tempo track to match, was the (rubato) tempo of your original playing o.k. for you (i.e. before quantizing)?
If only the ramp function would make smoother curves with closer points it would work easier.