Last Chance Canyon NM from El Paso TX: driving route/time beta?

anyone know what the driving time is from El Paso airport to Last Chance? I see it's 193 miles if you take the 62/180 east and then northeast almost all the way to Carlsbad, and then cut west on County Road 408/Dark Canyon Road, and then south on 137/Queen Highway. Is that the best way to go? seems like a long way out of the way, but perhaps it is the fastest route.
I'm planning a trip in April, and would appreciate any route/time beta. Many thanks