Ideally, you should leave the tips thick and wide from the start. When making a bow, the tips and handle areas are the last place I work before its all done. That way I can make corrections after the bow is strung for the first time or even after it is shot.
I make the last 6" of each limb tip static(non-bending) I start the taper there and go out past the string grooves. This last 6" to 8" is where the extra weight effects the hand shock. Everything beyond the string grooves is dead weight also so most of it can be reduced. There is no pressure beyond the string grooves anyway.
You probably can add long wedges to the tips(as overlays) on this bow to beef up the thinner tips. Any good hardwood will work. Make the wedges about 4" long(thick end towards the tips) and be sure the glue mating surfaces are flat and well matched for good glue adherences ....or leave this bow alone and make another using thick, narrow tips.
Pat