I know the stretch immediately below Pagosa is called Mesa Canyon and is considered class III-. However, I have not floated it, and do not know what lies below there.
There was this quick blurb about it:
NAVAJO RIVER NORTHERN NEW MEXICO- NAVAJO LAKE STATE PARK
One such example is the 25 mile Navajo River run from Dulce New Mexico that during high water runs into Navajo
Lake and Navajo Lake State Park that only gets water when the Azotea Trans Basin Tunnel is full. It bears
scouting the entire route. The river above the lake is not administered by New Mexico State Parks.
on this website:BoatingwatersriverrunningNewMexico
hope that helps!