Solving the problem of a ringing/ buzzing string
My Dominant A string used to ring a little as the grooves in the fingerboard became too deep. I've resorted to placing a small piece of cloth in the groove.
However, would this cause a new string to deteriorate faster? What other solutions would you suggest?
Absolutely getting a qualified luthier to surface you fingerboard to get rid of the grooves, I charge $20-30 depending on whether its warped as well or not.
I suspect that our OP is referring to the notches in the nut when he says "grooves in the fingerboard." Otherwise how could he build them up with cloth? If I'm correct then you might build the notches up with some CA glue, but it would certainly be better to have a luthier look at it.
Again, A $20 repair, I remove the nut, glue it back in place with a piece of paper or thin piece of veneer under it to raise it up just a fraction, then use black marker to colour the paper or veneer so you can't see it, all glued with hot hide glue, saves the much more labour intensive fitting of a whole new nut.
Prices on resurfacing a fingerboard, or altering or replacing an upper nut can vary widely, partly depending on what method is used.