If the work is just adjusting the brakes, you don't specifically need an RV service business, you need a trailer service business. Yes, RV shops work on travel trailers, but there are also lots of places that work on all kinds of trailers (such as cargo, livestock, etc) and would be very familiar with the brakes, even if they don't do general RV work. All of the Escape running gear (axles, suspension, wheels, tires, coupler) are common trailer components used on all sorts of trailers.
If I were calling business to ask whether they do this sort of work, I would ask if they do brake work on Dexter 3500 pound trailer axles.
As for the vicinity of Gig Harbor... sorry, I don't know anything businesses in that area.