I faced a somewhat similar situation a couple years ago when I made a natural edge coffee table from a myrtle burl. The burl had so many holes in it that I took a photo of it with pencils sticking out of the holes and it looked like something from a crime scene investigation! I bought several tubes of slow set epoxy and mixed it with artist's oil pigments and it worked very well. You can, of course, see the difference between the wood and epoxy but it didn't detract from the beauty of the finished piece.