I would suggest that the WB breeders study what has happened to the American riding & light harness horse breeds.
Morgans and Standardbreds started with a TB stallion. They got a type of horse that had non-TB characteristics, and they decided to emphasize the non-TB characteristics and bred descendents of the F1 males–Justin Morgan’s sons established the Morgan breed (TB sire). As far as I know there has been no TB infusion since the first 2 (?) generations of the Morgan breed.
*Messenger’s grandsons, from native trotting mares were used to establish the Standardbred (or is it great grandsons, I’m tired, forgive me.) In the 1800’s there were heated discussions on how the TB killed the Standardbred trot and how the Standardbred breed no longer needed anything from the TB.
The gaited breeds are descended from American horses, often with copious infusions of Morgan or Standardbred, so their TB blood is usually extremely distant in the pedigrees of today’s horses.
When Americans ended the infusions of the TB blood in their breeds, their breeds became specialists, the Morgan specialized in being the most versatile American breed, the Standardbred specialized to harness, the gaited breeds specialized in being superior “park” quality easy gaited or very flashy riding/light harness horses.
Of course the QH is also descended from a TB sire line. The QH also became specialized, as a reasonably versatile Western horse. However, since QHs are FAST, TB sprinter blood was allowed to come in, muscles with fast-twitch fibers mated to muscles with fast-twitch fibers, to form the Appendix QH which can be a quality riding animal for sport in the hunter/jumper field, especially as lesson horses!
What the TB blood brings in is OPTIONS. Galloping ability is improved–the TB specialty is the gallop after all. I’ve noticed in the Holstein how the TB outcrosses lengthened the croup, put in decent withers, deepened the chest (more lung/heart room) refined the neck, and increased the length & slope of the shoulders. AND (I know I speak heresy,) improves the jumping ability.
I am sort of puzzled by the comments I’ve read about the TB bringing in intelligence and endurance. Yes, some TBs have very good brains, but when I was young their reputation was the opposite. Compared to the Arab, Morgan, American Saddlebred and QH the TB was considered crazy and sort of dumb, and harder to train. TBs were for the more advanced riders. Half TBs were OK for lower level riders, 3/4 for better riders, then full for good riders. The TB brings in athletic ability, not brains in the USA.
Endurance? Arabs of course are better, but for long rides not at top speed the Morgan does quite well, as can the ASB & other gaited breeds. Standardbreds have a well earned reputation as being tough and enduring (heat races, 2 out of three.) TB endurance is for long gallops, but an equally fit Arab can gallop for a far greater distances near their top speed, and I suspect an equally fit Standardbred would be keeping pace and distance too, though at the slower trot or pace.
BUT, if I were able (I can’t) to ride cross-country at a gallop over land that neither I or the horse had been over before (not a groomed course), I want a TB under me. At the unexpected disastrous jump the TB can react to the situation quicker, alter the strength of their take off, stretch just a little further, recover from a bad landing better, and keep on going several miles at the hunting gallop.
And this is lost the longer you go from the TB blood. Gallops, athletic ability, a certain amount of endurance, and when that is gone it stays gone. Sorry.
Or you could compromise on height and go to the PURE Arabs. Russian or Polish Arabs would probably be your best bet.
Good luck. Your present horses are IMPRESSIVE!