Well Wooly that helped a lot I would have bet you by the first pics that it had a grey primer on it. I would try the steam but be very careful not to leave it on for too long as it could loosen the glue on the veneer and then you have a whole new problem. Maybe if you can get them closer to the top you could stain with a black dye mixed with alcohol instead of water. Using alcohol in the dye will not raise the grain as much and will require less sanding back. By doing this you could get some black timbermate or similar grain filler and fill any void not corrected and then sand back carefully with steel wool or high grit paper and then stain whatever color you are using. That will help pop the quilt and possibly make the spots less noticeable like they are part of the figure. Just my 2 cents. You can check out pics on my build and see my tele stained dark and sanded. Ack before applying color and I used Keyda power aniline dyes I got off of amazon for cheap..