Some quick advice from a Pencilhead who just left Lafayette in December... (not a flight major).
Don't expect to be able to instruct at Lafayette Aviation (unless you've already got a job there). Jeff Pittard is a bastard and that place is just all around shady if you ask me (well, the flight school part is). There is a reason that this January was the first time in the history of that company he has had a flight instructor there for more than two years.
Instructing for the school is truly part time--and I'm sure you know it. Personally, I couldn't instruct there due to some of their policies regarding the teaching of certain things... But at least you know that you get to fly truly excellent equipment, you get a set amount of flying, and you are no doubt familiar with that system.
You probably know about the Beechjet already. It is a very remote possibility. And some of my best friends flew the Beechjet, so I know what a really awesome experience that is (and I hear they are going to type the new class again now).
Here is why I left Lafayette when I graduated in December.
1)I'm a mountain boy, I was really tired of IN
2)Only real options for working as an instructor were Lafayette Aviation, and the University.
3)There is NO possibility of multi-instruction anywhere in the area (Lafayette Aviation has a TON of MEIs, and PU onlly has full-timers in the Duchesses)
4)There are WAY TOO MANY young, hour mongering CFIs there to be able to really get a decent job
5)I don't think real highly of many of the pilots around there--a lot of people who think that flight program really makes them a stupendous pilot (I have flown with a LOT of PU pilots, and I was on the flight team for a rather long time--yes as a non-flight major)
My advice would be to leave as well. Sure, keep going to school, but I'd go someplace else. I'm thinking of going back to school myself, but I don't want another degree from Purdue. You can find another decent school someplace where there isn't a pilot-mill around and they won't be so flooded with flight instructors. Even Indianaplis would be a better place if you ask me, a lot more people there learning to fly for fun rather than as a career (as in Lafayette).
Drive around, knock on doors, stop at every airport you see. And don't carry a chip on your shoulder because you went to Purdue. If anything, I'd say you've got a long, hard road to learn how to fly airplanes like the rest of the world. But you can do it, it'll just take some work.
Good luck!
Dan
PS-I couldn't tell you about the intern thing, but even with a LOT of intern experience, I would not expect anyone to hire someone with 300 hours, the biggest twin actually being flown (as a competent PIC) being either the Duchess or 5DA at Lafayette Aviation.