Maybe consider A&M where financial aid seems to be more generous (for a wider student group not just super high stats or 0 EFC).
Generous merit aid (at UT only for super high stats), a very generous aid package for National Merit Finalists (UT has none) and also aid for low income.
Read about The “Aggie Assurance” http://financialaid.tamu.edu/Aggie-Assurance
A&M has a fantastic Engineering Program just like UT does. Other programs are good too. So, the school is another option in TX besides our flagship school.