Pre-Engineering?

I want to do research in something along the lines of bio systems engineering. I really like NCF’s academic environment, but they don’t have engineering. Would it be feasible to have a nat. sci. or physics AOC and go for a master’s in engineering? Would I be able to get into a decent grad school?

Also, if not, what about going for a year and transferring out. I know that sounds insane, but I’m in a bit of a bind. I’m about to graduate community, and have too many credits - thanks to the predominantly useless 30 AP credits I took - to stay in a two-year program. Out of many universities I’d like to apply to, my lack of a physics pre-req either disqualifies me completely, or makes me uncompetitive. So I thought I might go somewhere else that I can get those pre-reqs and apply to my top universities, and if I wasn’t accepted, I’ll still be happy at that college.

I’ve been told that it transferring out is very hard, that will be difficult for my contracts to count as credits elsewhere, and that my GPA shows up as 0.0. But I was also told much of the difficulty with transferring was that most people who do so make the decision quickly and are unprepared. If I knew ahead of time I may do this, would transferring out be feasible?