Google Maps says I-44 to Wichita Falls then 277 to 180 to 62 is 810 miles. The is the southernmost route.
Or.. I-44/40 to Amarillo then 60/214/82/62 is 824 miles - the northernmost route.
This time of year watch the weather closely. We'd take the southernmost route.
Are you going anywhere else other than Carlsbad? This is a crummy time of year for that trip.
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Full-timed for 16 Years . . .
Traveled 8 yr in a 2004 Newmar Dutch Star 40' Diesel
& 8 yr in a 33' Travel Supreme 5th wheel
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