Yup, engineering majors have a boost in LS admissions IF they have similar GPAs. A 3.8 liberal arts student is more attractive than a 3.65 engineering student in most cases for selective LS admissions.
U New Mexico should be affordable. New Mexico Tech is better than it should be, and also might be within budget. There are others of course, but getting to ABQ should be simple, yet it will feel “away.”