That looks ideal to me. Piking it will do 2 things. Increase overall draw weight, and increase the amount of weight gained per inch of draw in the last few inches of draw, or more simply put, increase stacking.
If you want to see what piking it will do without cutting the tips down, cut a small block of wood and glue it where you want your new tips. Shape it so the mating surfaces match the curve of the recurve. You can then carve a string groove in the block and make a new string to fit.
If you arent looking for a change in performance and are only concerned about the string coming off and want to redo your tips here is a good looking idea. Just like you did an over lay, gring flat the sides of the tip and do a side lay. Then do a new overlay on top of that. Ta Da! Brand new tips. I have done it and it looks beautiful.