> Am I deluded to think that there's a job out there that would allow me to utilize most of the skills I've learned, and learn new diverse ones?

I currently am in such a job. I'm doing a very diverse range of things, from schematic and layout design to web programming (although I do the latter rather dreadfully). It is a fairly large company and not my ideal job, precisely because it is in a large company, where everything is slow and bloated. An guy I used to work with a another company was employed here; he recommended me to his boss when he heard they needed someone with my skills, they called me for a quick discussion and offered me the job.

I also had a similar job in a startup company a while back. It really was my ideal job. Bad business decisions strangled it after about two years, unfortunately. I landed that one via the boring route -- job ad on a website. Applied, went to interview, got the job.