First, how expensive is that sonic tomography machine, if you don't mind my asking, and how well does it work?
There are four sonic tomographs on the market, the ones I know range from about $12 000 USD to about $20 000. They work quite well but have their limitations and operator knowledge is very important. You should also have a resistograph (another $10 000 USD or so) to confirm some of the tomograph findings. The truth is you cannot visually assess the cross-section of a stem without advanced equipment.
Also, what does the presence of ant holes indicate?
Ant holes indicate the presence of ants and therefore the presence of decayed wood. You must understand a little about ants to interpret ant holes. There are a couple of general books to start with:
Ants of North America: A guide to the genera by Fsher and Cover
A Field Guide to the Ants of New England by Ellison, Gotelli, Farnsworth and Alpert
More Detailed information, and likely more important for tree structure is:
Carpenter Ants of the United States and Canada by Hansen
I just climbed a black walnut tree yesterday, and when I cut off one particular piece of deadwood, maybe two inches in diameter, the ants just came pouring out of a tiny hole in the dead center of the remaining stub. It was the only piece of deadwood in this tree that had that happen. Do you think this might mean the tree is in a great state of decline? Any insight you can give would be greatly appreciated.
Ants in a limb/trunk indicates that decay is present but you must also assess the extent of decay and the tree vigor/vitality. The mere presence of ants is not a significant hazard but it is a signal that you need to know more. If you are going to consult you should try to determine the Genus as this can tell you a lot about the ecological niche and may be a clue to reading the tree.