My last input in this topic, since most of it doesn’t have anything to do with OP’s question.
Goodhors: I’m glad I misunderstood you when you spoke of “big hooves” 
TWHs gaits: It is utterly ridiculous to assume that TWHs do not have the trot or pace as one of their gaits. The vast majority of the TWH foundation stock were racing champions. Some were the trotters, others were the pacers in harness. Sire F-1 was bred to be a trotter, but turned out to be a pacer. F-38, son of F-1, was a trotter (the trot was one of his 7 gaits).
In the last 2 decades, when evaluating young stock, the best natural pacers get singled out: those are the ones who will end up on pads - and if they do well they get awarded with a lifetime of stall-bound life on those pads. Since the gaits are mostly determined by conformation, it’s not hard to breed for the pacers.
To accommodate owners/riders who have horses that are not very inclined to canter, most classes are divided in 2: one for those who do canter, and one for those who don’t. However, the big lick class includes the canter always. If a TWH couldn’t canter, they certainly wouldn’t be famous for their rocking chair canter…
Suitability as an endurance horse: I’d like to go back to foundation sire F-38, whose job was to deliver mail - 38 miles each day. In the evenings he would get rigged up for races. It was not unusual to find him at county fairs racing during the day, and winning the gaited classes the same evening.
For a more recent example, Gypsy Lane Bigshot won the 2008 Santa Fe Trail Endurance Ride, winning 2 individual race days, and 3 “Best of Condition” awards.
A well-conditioned TWH, with his running walk well established, can easily travel at a speed of 8-12 mph for hours without breaking into a sweat.
As for the remark by Easysteppin that as a breeder I am apparently changing the breed’s standard: I’m happy to say that I am one of the fortunates who are still breeding true to the old lines - not only that, but also very close to the old lines. In fact, I am continuing a breeding program started by one of the most influential breeders of the TWH who was part of establishing the breed.
OP: In the TWH you will find a very capable and willing partner. But, if you plan on jumping, there’s one conformation issue you need to pay close attention to: A lot of gaited horses of any breed have a very mild version of sickle hocks. This is not detrimental for their gaiting capabilities and causes no issues as such. However, lots of jumping will eventually cause joint problems.
I loff ponies. Now WHERE did I put that winning lottery ticket?