Quite a read, good for you that you seem to be this passionate, specially about something as awesome as programming (or maybe computer science in general).
As for reinventing the wheel, it's not necessarily bad at all, it happens to many of us; some of us get over and learn to reuse, some others don't. One other way you could test which camp you're in is going all the way to the (high-level) bottom and work at the operating system level, so maybe you should take a look at C/++ and see how you like it.