Instead of a massive wall supported by electronics and huge numbers of agents why not a basic wall like what is currently being used and add something like 5 acre cross fenced square lots all along the barren areas of the border with retired Latin Spanish speaking veterans living, initially in propane powered FEMA type housing on each lot? With intranet connections and webcams everywhere, these people could greet those making the dangerous trip across the border. The veterans could then contact agents to come pick them up. Not to toss them back across the border but to place them into acclimation and training centers all along the border within the DHS controlled border buffer areas. This could partially be paid for by tolls, much like cities do for new bridges that pedestrians as well as auto traffic pay both ways for. Expand border crossing areas laterally along the border and treat all traffic like the Columbians do. Everyone gets scanned going either way and all items, including vehicles, get a thorough inspection. Don't seize peoples property to do this if at all possible. Swap them federally owned land abutting what they have at something like 2:1. If DHS takes 5 acres, they get 10 in return. If reservations refuse to cooperate, place the 5 acre lots all around the perimeter and treat all crossings as though they were border crossings.
These people could also be trained to help develop the infrastructure needed. Considering the sparse populations in these areas this may be the only choice for labor. If they pass the retention period of say three years, then they could receive special visa's that allow them to move across the border without further vetting. With the type of training they would receive, including Americanization, when they go back to their home countries they will hopefully want to implement it there.
Set up a no-build zone between the 5 acre DHS zone and everything north of there as something like this will no doubt drastically change the number of people and businesses all along the border and interloping and trespassing could become an issue.
After a period of time the FEMA housing could be replaced with permanent housing and a two way rail system could be created within the zone from East to West. Besides supplying for internal needs it could be invaluable during periods of natural disaster of national security without the involvement of outside issues.
For labor to initially build this why not look into volunteers from the retired/disabled community of people who have the skills needed to do this. With a shortage of skilled labor, especially in these remote areas this may be the only affordable way to do this. Set up camps with needed medical facilities and the number of people ready to help do this may be surprising.
Just an idea of course.