From what I know it is against state law the dig or even pick up & keep artifacts, becareful and if you moved and brought your Texas finds to your new home make sure you can prove that they were found in Texas .if they the state get on your trail and have a woody to go after you , they the state have the power to come to your home & search and take all artifacts , includeing your Texas finds if you can't prove they were not found in new Mexico ,I know a couple of buddies in hobbs who surface hunt and are very hush hush about there hobby , so if you do go looking remeber the state looms over head . Good luck.
As a back up to Blackwater Draw, you need to meet some ranchers in the area. There is private property around in addition to the Fed lands. Surface hunt the blow outs in the sand hills. There were usually sub surface artesian water sources in the sands; i.e. Artesia, New Mexico. As a kid I grew up surface hunting in SE New Mexico, and especially along the Hondo River just west of Roswell. It was exceptional. If you can locate what was known as "Brown's Ranch" west of town it could be worth your while. I haven't been there since the mid 1960's, but the ground was littered with broken pottery (both an unpainted brown similar to Leon Plain and Chupadero Black on White)in the same fashion central Texas campsites along rivers are strewn with broken mussel shells. Mostly arrow points with incredible lithic materials. Real colors, not shades of brown and grey. Also surface hunt plowed fields just off the caprock as surface water used to be abundant at the base of the caprock.
I'd definitely talk with ranchers/farmers, might be tricky with deer season on....I live in tx panhandle and surface hunt various sandhill areas near tx/nm border...focus on playa lakes and what natural landmarks you may find visible from a long ways off