Hi. As a mostly ex fiddle player I understand what you say about the hardened and in my case shiny pads. I had the same finger slipping off the buttons thing happening, mostly the ring and small fingers on the left hand and predominantly on the inside row although the ring finger on the D button in the middle could be vulnerable. So the first thing I did before I’d play was to give the pads of my fingers a sort of buffing with an emery board or nail file. The cardboard ones or disposable ones, about mid roughness. It was just to ‘key’ them as it were and definitely not a skin peel or plastic surgery!! This worked to a degree. I have to say though I was so frustrated that I entertained taking a rasp to the top of the buttons and roughing them up!!!!
However I learnt that the issue was more a sensory or mechanical one than a skin issue. It was about how I put the finger on the button. I don’t know about you but I was trained to arch the fingers over the fiddle fret board and press down with the very top of the finger and I just never gave the action of placing it on the buttons a second thought. For me, I found it to be very subtly different. Same muscles and action probably but in the last mili seconds and millimetre there is a different connection on arriving on the button. So it was about slowing down and noticing the finger arriving on the button. I would practice just bringing the finger down and noticing the contact between finger and button.
Off centre would a bit of a problem alright if you are doing it all the time so that exercise should correct that but if you have the rest right and the landing is correct you’ll get away with the odd off centre because you’ll catch most of the button.
How you hold your fingers over the buttons when not using them might be an issue. Again if you are repeating the arching it might be causing a problem because I noticed that a lot of the better players keep the fingers extended, presumably in a relaxed way, over the buttons as opposed to being arched ready for action. But I feel an awareness of the minute contact on the buttons will fix it.
I hope this helps in some way and best wishes.