Strangely enough, I actually did have this sort of problem while running my school anime club. I blame the old school projector, where does the budget go?
In any case, my HDMI to VGA adapter (somehow) works in full HD. I sadly can't give a demo, for I tend to leave my laptop at school(It literally needs an external keyboard, I'm not taking that thing home). According to what I have seen, DVI is superior to VGA, so... yeah. There is a really good change that the adaptor should work for higher qualities.
P.S. Heard good stuff about Cable Matters. The link he shown seems to be a good deal.