Oh there's several better ways, some of which they've been testing and some of which I've played with. The problem is they haven't bothered to try to embrace anything new, especially not for traveling, say, past the bloody moon.
You mentioned you were graduating in a few months, so you'll have that degree at least? However, it's not going to make them listen to you, if you have ideas that might stretch their budget. Maybe try something private sector first, lad, and then think about NASA once you get some solid testing done with some results to prove to them something will work.
As long as you don't inadvertently blow up part of Texas while attempting to prove a theory is correct, you should be fine. But that's all I will say about that matter.