My son was accepted in September on the basis of EXPLORE test scores and a portfolio of above-grade-level work (we also homeschool). Someone suggested once to me that if you live near a local university, you might be able to get testing done by psychology grad students at a greatly reduced costs. Also, if you submit a portfolio and application that piques their interest, as I suspect this would, Davidson would offer some ideas (maybe even aid? though I say that with no actual knowledge) for testing or other missing information. I would go ahead with it -- my feeling is that if they see promise, they'll figure out a way to help you the rest of the way.
Karen DV
