There are political opportunities everywhere and they range far behind what you describe.
My kid did a DC semester. Had 7 offers to intern. 7. Full time. She is at College of Charleston - it’s not for you because of cost - but if you look at the government, the Trump trials alone - I saw Christopher Newport, Kent State and more as major players. Charleston had a Trump staffer, etc.
So you can have that too. You’ll find state, city, county, non profit and more in college station/bryan or other areas in and outside of Texas.
If you want to go without debt, Texas has many fine schools. You can try for merit at places like Trinity and Southwestern.
Or you can go for Hail Mary scholarships - highly unlikely but you never know so throw an app knowing you’ve already got a great one in the bag - Wash & Lee Johnson, SMU (on your list) Presidential, and others have full rides too.
Or go where it’s less expensive - many public schools all over the country.
A&M is a fine school - but there are many fine schools where you can easily accomplish what you want - including A&M. But if it’s not there, choose one of the other fine Texas or non-Texas publics or LACs that can get you $40K or less if your parents can stretch. I read somewhere Rhodes is getting people in $30K or less (if you can stretch) and another commented to me the other day they under enrolled - will they pay up more?
I think your black and white view about finding opportunities is very far off the reality is what I’m saying.
And I agree with your parents - eschew debt - especially given the major.
And you have a budget - so stay within. If you want to go outside, hit Ole Miss as mentioned earlier - and you’ll stay within budget.
Basically you got the cake already. But you have the chance to add some icing.