My son has a close friend who plays bass and wanted to double major. Although quite accomplished in both academics and music, he did not get admitted to most of the schools to which he applied (some mid-Atlantic, some Midwest). I think the programs are small and faculty few, to which you alluded. He did find a decent fit in a good school with a strong conservatory but got more rejections than expected. Just to say that I would seek advice from those in the know as I think the double major programs that might rise up as most appealing if you are seeking a top musical program as well as a strong academic climate may be quite competitive simply due to having very few spots. A minor would be a very different scenario, I would think. Best wishes!