I graduated from Parks College of Saint Louis University in 2001. The flight program has changed quite a bit since then, but it's still a great program. The Engineering program @ SLU is one of the best in the Country. I would definitely go with your proposed course. If you can do the Engineering major, I would just get your ratings on the side or do a double major/major minor.
Since it's a Private Jesuit College you will have to take some religious courses, but it's usually just Theology with options for more in depth courses. If they're offering you a good scholarship/financial aid package, I'd take it and run. It's a great school with an excellent reputation, and there is a ton of stuff to do in St. Louis. Although that is sometimes more trouble then anything. I missed & slept through a lot of classes due to Penny pitcher night at Humphreys.