So pay for it with public funds, and keep private profit out of it.
I'm a Vermonter so I don't really have a dog in this fight but it seems to me that even if Texans never used this highway they would still get a great benefit from it. If all of the truck traffic on your current highways is shifted to I-69 would that not make your travelling easier?
If it kept the Mexican truck drivers of questionable competence off your highways is that not also a good thing?