For future reference.....the CA approach is fine, but costly over a large area, particularly if you need to take several fine cuts off the surface and then require a second treatment of the grain. There are cheaper alternatives, such as giving the surface a good coat of cellulose sanding sealer, or even a proprietary wood hardener sold by companies like Ronseal and Sika, readily available in large DIY outlets.
Whatever approach, one basic rule always applies.....fine cuts with sharp tools!
Les