I myself, never set out to be a live virtuoso...as I was more into the writing and the creative aspect of song writing.I have, however, always made an effort to sound as natural as possible in my quantizing(when the genre of music called for it.)
I would only quantize what needed to be quantized and of course,certain tracks must be left natural,such as solos.As for becoming stiff,that happens when you do not play regularly and quite possibly...performance anxiety is a contributing factor.
The composition of this tune is very pretty,but may I suggest that you at least quantize at least one of your tracks?This would probably make your performance easier,when you are playing along with a track that has good timing.
I think that when you add delay to a track,it is especially critical,to ensure the timing is good,so the performance matches the timing of the delay.I know that certain individuals are adamantly dedicated to going completely natural,but I remember something my music theory teacher taught me in high school,which is that...without rhythm,there is no music.
Ironically enough though,that teacher had terrible rhythm!