I ended up doing some testing on the bottom side of the table. I decided to fill the insect damage and knot holes on the bottom of the table with a coat of epoxy colored black with some pigment.
Here's a picture of the table prior to the epoxy pour:
Here's a picture of the epoxy pour:
Things looked pretty ugly at this point and I wasn't sure how the boards were going to take oil after sanding off the excess epoxy.
Here's a picture of what it looked like after sanding off the epoxy with a round of sanding at 80 and 120 grit:
Here's what it looked like after two coats of tung oil (first coat was cut with 50% mineral spirits, 50% tung oil along with a little dye that I added to help darken the boards a bit):
I was happy that using epoxy to fill the holes didn't seem to affect how the boards took the oil. The only negative effect is that if you look at the table from a certain angle you can see that the grain is completely sealed in the areas where I used epoxy where some of it is open in other areas. I'm sure I could have corrected that by using some sanding sealer or just skim coating the entire table with epoxy instead of just certain spots.
I also made a mistake with the dye / tung oil mix. I'm sure the transtint dye I used was a mistake as it never fully mixed with the tung oil. I'd have to stir it before wetting my rag. I forgot to do that once and had a bunch of small dye pieces that caught the top of my rag. When I put it down on the dry wood the color set instantly. You can see that mistake 4 boards in from the left, about 6 inches above the dowel. If I use this method for the top I'll probably take the rag I'm dipping in the tung oil / dye mixture and wrap it inside of another rag before applying.
The other thing I found interesting was that using the pigmented epoxy to fill the holes looks much better than the black Starbond CA glue. The pigmented epoxy gets darker as the hole gets deeper. For the thinner parts of the holes on the leading edge the epoxy is slightly transparent, showing the grain of the wood underneath it for a while until it eventually turns completely black. The black CA glue is solid black no matter how shallow or deep the hole is.
I'm happy with the testing done on the bottom of the table. Hopefully the top will turn out a little better.