Looks like about a day per segment.

Belen to Ft. Stockton is a fairly easy day. Providing the traffic in El Paso ain't too bad. Interstate all the way. Probably 6-8 hours.

Ft Stockton to Laredo seems like it might be the longest and you are probably looking at something between 7 and 10 hours. Mostly on two lane roads, with limited services.

But it all depends on how fast you drive, road construction, Pit Stops, food, etc.

60 minutes difference from the mapping programs is well within actualities. for a trip this long, 60 minutes ain't gonna amount to a hill of beans. YOU WILL BE DRIVING ALL DAY ANYWAY.