I don't have a website, I'd look for books ... kinda sucks if you don't have access to an academic library. You could both check out the books of Gardner himself (the introduction and conclusion
or educational books about intelligence and more generally differential psychology and personality theory.
From my feeble academic experience, I'm gonna try and clarify this. What you will find in the direction of "proof" is basically that the new model is more suitable to explain the empirically measurable performance of people in various settings, statistical stuff. You'd have him compare the iq of people correlated with their learning ability in various things. And then in comparison the different forms of intelligence. The proof would be if the new variables correlated significantly higher with actual capability in model-conform areas (i.e. skill1 + skill2 = capabilityX) than does iq.