Hi Benjamin Strange, sounds like a fun job. What exactly are you doing for Mesa?
Here's my take on schooling. I have an honors degree in engineering from a prestigious Ivy League university. All things considered, I'd have to say that hasn't helped me "at all" in terms of musical electronics. Everything I learned about electronics as it relates to music, I learned outside of school. It's something along the lines of "street smarts".
However, the formal schooling has definitely helped me in other areas, both in terms of work, and outside of work. There's hardly any downside to getting an education.
Where to start, would depend on how much you already know. For instance, I've been dinking around with electronics since I was six. Started with the Radio Shack 101-in-one kits, then moved on to ham radio, then on to computers, and so on. By the time I got to college, I already knew everything there was to know about tube amps. Built 'em, designed 'em, fixed 'em, etc etc. You can do all that without one spec of formal education.
Where the formal stuff really helps is in the more esoteric areas, and those with a lot of math. Waveguides and transmission lines would be an example. Those definitely have applications in audio engineering. The theoretical areas like materials (how to build chips and sensors, like if you're interested in piezo pickups), antenna theory (which it turns out actually relates directly to how much hum you're getting out of your bass and your amp), and very basic physics (like "grounding") also have some applications in audio engineering. Those areas are kind of esoteric though, and eventually if you build enough tube amps you'll probably cross over into some of those, but they're not needed to understand a schematic and how an amp works.
My suggestion would be, concentrate on the "basics" in your first year, or couple of years, in school. Math, physics, chemistry, that kind of thing. Those are hard topics, 'cause you'll be competing for grades with the pre-meds and the hot-shot engineers, but as long as you're willing to dedicate the time, you'll do fine. Then, while you're doing that, pick up some books like Gerald Weber's "A Desktop Reference of Hip Vintage Guitar Amps", and the "Audio Cyclopedia", and that kind of thing. While you're reading those, pick yourself up an old beat up vintage tube amp (the cheaper the better), and try modding it with some of the circuits and principles you encounter in those books. There's no substitute for practical experience. The more time you can spend with a soldering iron in your hand, the better. You'll know when you're ready to start designing stuff.
Once you have some experience like that, "then" decide what direction you want to take in terms of your last couple of years in school. Typically the latter half of the degree track is "specialization". so you'll probably have to pick some area of electronics that you want to be an "expert" in. If after your initial exposure, that still turns out to be tube amps, then go for it. But who knows, you may discover that there's another area that appeals to you more, like maybe the electronics of mixing consoles, or music synthesizers, or computer music, or something like that. What I'm trying to say is, test the waters first, before you jump in.
Man, that sounds like a great effort. I wish I had the time to go back to school. I have a part of a PhD in neuroscience, and through a strange turn of events, my advisor ended up going abroad on sabbatical, and I ended up playing music in a rock 'n' roll band. Thank God I had some electronics education to fall back on, 'cause after I got burnt out touring there was this big question about what to do with the rest of my life. So I became a third party field service engineer for computers for a while (this was back in the days of the PDP-11 and such), and that's the direction my career has taken ever since. These days I make a big fraction of my living as an electronics consultant to studios and such, and the rest of it comes mostly from software services to non-software sectors of the industry (like healthcare, access control, the financial sector, and so on). There's more money in the latter, but the former is a lot more fun. I often end up dinking with someone's tube amp till 4 in the morning, and then arrive at the client site "just in time" for the morning meeting.
Anyway, it's a wonderful thing when you get to combine your work, with something you really enjoy doing. That's a real blessing, getting up and going to work every day to a job that's actually "fun". A surprising number of people don't have that in their lives.
I wish you all the best of luck and success with your endeavors.
Help a brother out - I might just end up designing your next Boogie amp! 
