I am not a web designer, and never claimed to be (although my business card says I am, mainly because I update our new site through proprietary programs, none of which is a direct html/java/css whatever editor.)
I know a wee bit about good design.
You CAN teach prepress (or xml, etc.) but I would think that if I were to plunk down $25-40K + benefits and perks on a new hire, I wouldn’t have to teach him the basics, yeah? teaching good design to somebody with no initail talent is like teaching a chimp to type. yes, they may have the fundamentals, yes, they may be able to coherently string together nouns and verbs occasionally, but no, they will likely not learn the nuances of the art.
I have had a few “graphic designers” give me commercial work that needs hours and hours of prepress operation to make it usable. that just means that I/we charge the company more for setup time, no skin off my back. many GD’s can draw pretty pretty pictures, but few can do that and make them functionable. A good eye and the grasp of the fundamentals is what you (and employers) want, even if you are just “good” at both.
it may sound roundabout, but I guess I am actually agreeing with dozr, just coming from the opposite end of the spectrum towards the middle.
try to locate a school that will give you a more practical approach to design, sounds like you’ve already got a good grasp of what tools you will need in a job. focus on web-ready specifics in programs, and grab some freelance stuff where you can.
notes: skill + talent + examples = job. x degree = job x 2.