I don’t know that " gaited" is exactly the right word. They used to use the term “Ambler” to describe gait variations that created a very comfortable ride that got you someplace as an alternative to choosing between a pokey walk or bone jarring trot. Plantation Walker is a TWH term but descends from a pretty good description of what you want for DH… But I don’t know that you need to go looking for purebred anythings.
There are quite a few TWH crosses out there too. They tend to have the walk, just not on a grand scale. Some QH (and Paint, Appy) lines carry a tendency to "“singlefoot” but those individuals get sold as trail horses and taken out of the gene pool as far as shows are concerned but they are out there. Real working ranches certainly don’t mind them. Pinto registry is color based with a SS division and I’ve seen some that would certainly fill the bill for you.
IMO looking for a purebred anything might be going in the wrong direction for what your hubby wants and needs. And they can get pricey. He needs a middle aged ambler or singlefooter of any breed, cross or unknown ancestry. One long over baby boogers and not overly ambitious willing to amble along and enjoy life.
Might try asking around about working horses, not breed specific and not using the term " gaited" as some won’t understand what you are really looking for. Give that a shot anyway. I know they are out there, just saw two crossing the road on a local trail the other day…appeared to be QH/TWH influenced, one maybe a dash of Ayrab, ambling right along.