Hello Daniel and Teresa, I've watched this thread develop with interest. Much good advice above from thousands of miles of hiking experience. Lucky man. I'll add my 3K re: hitchin' along the CT.
I've been hitchhiking since I was 16. I'll be 61 this April. Like HB above, I've had wonderful experiences. And to be truthful, a few weird ones. (There was that state cop on I-80 in 1970 near Chicago. a-hem...)
When I was planning my 2009 CT hike I had several questions about road conditions, traffic, etc. I called some offices in CO where people work who might be familiar with the roads and trail. Like the DNR, Chambers of Commerce, Sports/Bike/Hike shops, etc. I introduced myself and told the person who answered why I called. More often than not, that person said, "Oh, you need to speak with..." and passed me along. I got great info that helped me make decisions.
There was a woman on here in the last year or so who was planning a hike on the CT. She was concerned about hitchin' to and from the trail to resupply. It occurred to me that she might make contact with some persons in those towns in order to secure rides. I suggested she call the sheriff or local police, the Chambers, the librarians, Rotary (Lions, Moose, Elk) Clubs, etc... anyone she could think of where she might make contact with someone who knows someone who might be willing to provide a shuttle for her. Obviously a cell phone, and service, are key. She, like you, had plenty of time to make contacts and make plans.
I'd suggest the same idea to you. You are a veteran. Google the vet's organizations around the state where brother or sister veterans, relatively close to the trail, might be willing, or know someone who is willing to provide a shuttle for you, et al. In your case, taking the dog may prove a bit more difficult to get a ride (unless perhaps in the back of a pickup). Additionally, as noted by them-there above, you're talking about A LOT of road walking... Some state highways where the cars and truck are really moving and sometimes the shoulders are fairly narrow. Your dog's feet may suffer. In my view, the money you'd spend for the shuttles will be well worth it.
The very best ride of my hitchhiking life was along the CT with a feisty old rancher who also happened to be a veteran from Korea.
RE: All the gear questions... Believe me, during those first few days on the trail, you'll quickly figure it out. (I mailed 4 packages home at the start of my AT hike in 2006... Stuff I just absolutely thought I HAD to take along. HA!)
You're a personable guy, Daniel. Make a few calls and get acquainted with some locals along the CT. I'm betting you'll make the connections and be off and back hiking the trail fast, instead of walking the roads to resupply.
Print this... http://www.pmags.com/colorado-trail-end-to-end-guide-2
And oh yes... Of course... HYOH! Good luck!