Couple thoughts....
You dont need to drill 8 inches, half that would be more than enough. Using epoxy is the correct product to use, I recommend Bonstone, they are not too far from you in Mukwonago, WI. Call them, they can have stuff to you next day if needed. Bell out the hole so its wider at the bottom, that prevents pull-out.
You should use a diamond drill bit. A carbide bit [i:e3b8b88a84]may[/i:e3b8b88a84] work but if it catches in the hole, it may break something and if that something is the bulldog... well thats not good. Same with using a tile bit, they are cheap and will work to drill hard stones, given enough time and water, but if it catches in the lava, it could be bad juju for Mr. Bulldog. I cant find a diamond bit to recommend so I would use a diamond burr, the only problem is the shank on those are so short. You will have to weld on an extension, it sucks, I know but it works and since the burrs are so cheap, if you mess up, its no big deal. Oh, and dont use a hammer drill. They are fast and easy but can also break the stone so in a high risk operation like this, dont use one.
When you drill, 3 rules: high speed, low pressure and cool bit. Drill it as fast as your drill press goes. Very low pressure, this is not a race. It preserves your bit and helps keep from cracking the stone. Lots of water keeps the bit cool, if it gets hot the diamonds go bye bye. You also need to keep the stone cool so it dont thermal fracture. Last, if your diamonds do away, you could end up melting the bit, causing it to mushroom over. When that happens, you cant get the bit out, the worst of all juju.
Adding weight would help deter theft. Have you considered mounting it to a piece of granite to match the headstone? Most headstones have a base stone to prevent mowing damage, maybe put the dog on one of those? If you do that, you can attach the dog to the granite base and then the granite base gets set in concrete at the grave. In order to take the dog, they gotta take everything, dog, base and concrete. Thats hundreds of pounds, a common thief not only wont but cant take that. Thats the way I would go but if the grave stone is a traditional military stone, it may not match (but you could still set the dog in concrete).
Its not a hard job, an hour should do it. Setup will take up more time and then a couple days waiting for the epoxy to dry.