I guess piano tone is something that is relative. I understand melody's position on how honkey tonk piano accentuates certain parts of the mix, evoking specific feelings. In the end, I guess it is your call if you want to keep this sample or go for something more traditional. It is probably the relatively bad input I'm listening on but it does sound a little bit high-heavy, like there's been some scooping in the mids. Will have to listen on a few different setups to confirm, but the high shelf shimmer right now is alright as long as the mids and midlows balance it out.
I'm not hearing the timing thing melody is refering to specifically. I will say the timing is, overall, very good, but there's some places where the left and right hands could do with some more alignment. This is usually at the beginning of measures, but it might be worth the time to go through with a fine tooth comb and tweak some of the timing to be tighter. I'm not saying make it sound robotic, but you're the pianist, so you'd know best where to tweak timing tightness.
The volume dynamics are very effective, but I do think a little bit of volume boosting during the quieter, less-intense sections would smooth out the track as a whole. I found myself turning up the track at the beginning and then had to go turn it down at 3:24 when it gets loud. Maybe not using a master compressor, but automating the volume to be a bit louder for softer sections. The volume, when it is at its loudest, is great - its just a bit too much of a contrast for me between the loud and soft. (Could also be the fact that I listen to lots of loud music, so that this advice with a grain of salt...maybe a few grains).
Reverb sounds pretty lush, no qualms with it.