Perhaps consider outsourcing some of the fun? Say, self-study a bit, but also bring on a mechanical or electrical engineer to do the heavy lifting.
If you do go for a degree, I'd suggest electrical engineering. I know many great programmers whose degrees are EE, and it sounds like you'll need some expertise in that area as well. (No, I'm not referring to people from schools where CS technically falls under the EE department, like MIT -- though a joint program would probably work too).
I think bringing in more knowledgeable people in the future will be definitely necessary. What I'd like to do is to be able to build a rough alpha version (think Apple I), and then have people come and polish it (think Apple II). With more people and funding, we may be able to achieve Mac-level (relatively, of course).
My problem with the full EE course is that it will eventually require me to go into areas absolutely not necessary at all. But the same can be said for all other options as well.
If you do go for a degree, I'd suggest electrical engineering. I know many great programmers whose degrees are EE, and it sounds like you'll need some expertise in that area as well. (No, I'm not referring to people from schools where CS technically falls under the EE department, like MIT -- though a joint program would probably work too).