Welcome to APC, Flyer. I have an AE degree as well and can definitely relate to your career quandary. You are correct the aerospace industry is in poor form these days, and it may be a while before it rebounds from the slump. The big question for you is, how much do you want fly? If on a ten point scale you are toward the 7-10 range, I would join the military as a flight training candidate on manned aircraft. This is easier said than done and there are many things to know about the path, but the idea is to generate turbine PIC time and thus make yourself a strong candidate for major airline flying when you eventually get out. Of course our nation needs aviators and an equally good reason for doing this is patriotism, but I believe the chances are somewhat slim for getting a manned pilot slot these days and you may only be able to get an Air National Guard slot with all the competition. It also will take some time (a year or more) to get started, so bear that in mind.
If military aviation is not possible due to physical limitations or something then I would think about engineering much more seriously. Without that military flight time you are at a huge disadvantage, you are going to be not very competitive to the airlines and you will invariably face a long, hard, slow, grinding struggle to get to a good job flying for a major airline. Rather than do that, I would stay in engineering. Think about using your engineering as a way to fund further flight training, and build the credentials to get on flying aircraft demos, aircraft production flight tests, or experimental aircraft testing. I have been doing flight testing, flight test engineering, flight test engineering support, and so on for the last few years. I has been a bumpy road since the recession cost me one job and seriously threatens another, but these jobs still exist and will always be around. I fly in my spare time, flight instruct, and so on. It is not an ideal flying situation but it is good enough. I do not have any serious turbine time and that is my weak point. I should have gone into the military when I was young and if I had I would have the turbine time now. I am thinking about taking another year off engineering to fly heavy (-er) aircraft just to build turbine time at this point. So, if you go into aerospace engineering wanting fly without any turbine time it is going to be a long haul although I have seen a few guys jump past the turbine PIC requirement occasionally. But don't count on it.
If you place yourself lower on the 10 point scale than around 7, I would not even think about flying either in the military or in the airlines. Try and get a job at Boeing, make kids, buy a Bonanza, and be happy. Engineering will come back in a few years and it has always been a good life. The problem with it is how boring it is, so you will have to either be one of these peaceful people who does not need much adventure in life, or else you will have to be a weekend warrior like me and keep your sanity by flying like a madman on weekends. Just my two cents worth. Good luck.
DE- glad to see you.