Nice playing I think you chose a good tempo. You could be a hair faster if you want, but this is good. I think popular pieces are popular for a reason, so no shame in playing those
Rather than trying a faster tempo, I think you can treat the pulse even more freely than you do - stay longer on the chords, go forward more on the eighth-note passages etc. This is supposed to depict some sort of (day)dreaming - a still, peaceful activity, but where all sorts of sudden emotional shifts can go on underneath the surface.