This is based on last year, but the process is probably the same. Both Cruz and Cornyn compare lists. They do not compare lists with every representative. Cruz and Cornyn do not have interviews, their board simply looks at the paper and decides. As a result, the student from something like Pecos ISD with 50-100 students in the graduating class (I don't know that-just guess for illustration purposes) who is a three sport letterman, student counsel rep, doesn't have much homework, works after school and gets high grades likely looks better on paper than the kid from Jesuit Dallas who is dedicated to one sport, already knows how to study effectively and efficiently, gets good grades, but has homework and does not work after school. The fact that the Jesuit kid is much better suited for the rigors of an Academy than the other does not come into play at the Senator level I don't think. (I just picked those schools because I have no affiliation with them) Last year I think they had about 600 applicants--I could be a little off on the number but not much. So, if you are not stellar on paper, or, have an inside in with Cruz or Cornyn where your application gets a gold star, it is a tough road. Yes, local reps sometimes give only one nom. Some give multiple. The nomination process is probably one of the few times that those who have purchased homes in affluent districts with top notch school districts are penalized for their choice. There is a much greater chance of nominations from districts that have lower public school educational offerings than the places where the school districts are uber competitive and filled with type A people. But, when we went through this last year, even at the local level, or maybe even more so at the local level, politics happens. If you know your rep, or if you know someone who knows your rep, use it to your advantage. But, even if your rep only gives one, they make exceptions at times. my DS received two from the same rep, who preaches he only gives out one. He gave a second because the Academy sent a note indicating that they needed nomination in order to provide appointment. Nomination was forthcoming within 24 hours of the rep's office getting the note. So, keep all your options open. And, remember, for USMMA, any rep in the state of TX can give you a nom.
With regards contact--Cornyn contacted with advise as to when the committee met, and then a note saying sorry. Cruz was a black hole and we received nothing from him after the application was sent. Got a different feel from him during the process as a result than his public political persona was. Good luck