TP, I think one thing to sort out here is this. There is a pretty big difference between an Aeronautical Engineering degree, and a run of the mill "aviation degree" with the emphasis that it is based on being a pilot.

Most "aviation degrees" are labeled something like aeronautical science, aeronautical technology, or aviation with the same science/technology moniker affixed to them. Sure sounds fancy. And although one may learn a lot, it's not really all that marketable. Sure, I know plenty of people with those degrees doing all sort of other jobs not related to the degree. But what I'm saying in this;

An ACTUAL engineering degree, regardless of discipline, is much more marketable than a standard "aviation degree"