The Big Lick gait is "manufactured."
Put another way, it's "nailed on" not "trained in."
Regarding Dressage, there is "Dressage" (with a "D") and "dressage" (with a "d"). The "D" means competitive walk, trot, and canter in a highly stylized setting. The "d" means little more than "training" and can be done in a wide variety of circumstances.
I've got a book on my shelf entitled A Dressage Judges Handbook by BGEN Kurt Albrecht. It's interesting reading. More interesting is that it includes a series of engravings from The Training of Horses for School and Battle by Johann Elias Riginger, published in 1760. Many show gaited horses of the day being prepared for military use using the same movements common in the Dressage/dressage horses of the day. The movements are also commonly seen today.
While today's competition Dressage is quite narrow in its scope, it has roots that go back far and wide.
Some time back the U.S. Dressage Federation was asked to consider adopting standards for "gaited horse dressage." They declined to do so at least in part due to the vast complexity of gaited horse movement. They felt it was difficult enough training judges to effectively recognize correctly done walks, trots, and canters. Adding the vast array of "soft" gaits would be unworkable. Given that even within some breeds there is no real agreement on what a given gait should be I think the USDF decision was reasonable.
This does not mean that breed or other associations can't create "dressage" tests and evaluate how well they are done. But it will be "dressage" not "Dressage."
Yes, the USEF and other Dressage governing boards/associations were what I referred to in my above post. Although there may not be agreement in breed organizations on what constitutes a correct gait, there are indeed very specific requirements on all of the gaits performed in any sanctioned Dressage competion, of any breed of horse (and now mules too). I.e. the requirements are not breed specific, even though the judges are taught the "typical" gaits of particular breeds.
So, as an example, I was able to teach my QH how to move like a "mini-warmblood" (quoted term from auditors in clinic) and also be extremely precise in my figures, allowing me to be competative against horses that had much better "God given" gaits naturally. The judges can absolutely recognize when a rider has improved the gaits on an Arab, Morgan, QH, etc.
However, the gaited horse has as stated many times, lateral gaits, and although some improvement may be able to be made on the quality of those gaits, I do not think it is fair to a horse to ask them to perform in ways that are so difficult for them. If one wants to do Dressage, then get a horse that has W/T/C. (IMO)
As for the difference between a capital or lower-case dressage, I don't see a difference. (IMO) Unless "dressage" is the word for training in the native language (which is not the case in USA), then it should only be used in the definition to mean the "systematic training of the horse by the training scale" (that was intended to be in brief).
If breeds with lateral movements want to test competitors in specific movements to show the correct training of a horse as evidenced by performance of defined gaits & figures, I really think that it should be called by another name. (IMO) Anything else is confusing to the competitor and especially the general public as a whole. IMO, there is enough confusion already with the sport, why add more? Many times I have heard, "Oh, you ride dressage; that is where you ride around in circles in a ring, right?".
I get a lot of flack from my fellow Dressage riders when I say I like gaited horses & I feel they have good points, so please do not think that I am a DQ that thinks all other equine sports are beneath me, nothing could be further from the truth! I enjoy participating in most all equine sports from driving to barrel racing! One time I even combined driving & barrel racing, but it was only for demonstration purposes only, I easily accepted that our time would be eliminated because I was did not have the required tack, i.e a saddle!
Another thing that one must always consider when reading books is, that they are not infallable either, nor can all books, no matter the quality of the source at the time, be correct for all ages. I balance what I read with my experience, and come up with what works for me. I could quote you books that describe in detail exactly how to throw a horse, including what kind & length of rope. "Throwing a horse" was the accepted way to start a colt for many years by many respected instructors. I would guess that there are not many equestrians today that would recommend or practice that method today. I love history & would enjoy spending more time reading about the horses & teaching methods of the past, however, due to time constraints, I really need to focus more on the here & now. No offense meant, and I would absolutely LOVE IT if you would consider sending me a list of titles of books that you have found to be of value. Seriously, please consider sending me a list privately!
I have rambled way too much now I see, and have gone completely off topic! Please forgive me...AA