US routes are higher order than state routes though
Mainline US routes are. I don't think we've ever established for TM if auxiliary (especially Truck) routes are higher order. My personal inclination is "no", especially since "Truck" isn't even an AASHTO-approved auxiliary. Truck US routes are designated and posted purely at the state level, which to me makes them no higher than state routes.
Personally, in this case, 262 is the better known designation, so I'd go with VA262.