grooves in chair bottom

I have two chairs that have grooves in the bottom that will make it difficult to tie off strands. In the past I have used some rock hard water putty to fill in an area or two to make the bottom flat. I have many grooves to fill. I would appreciate any suggestions. They are family chairs. Although I am a member of the guild, I am a hobbiest and do not do work for hire. I am certain this is probably not an uncommon problem.

Thanks, Jim Randall