Early on, schools of Swarthmore's ilk were my target because I wanted to attend school in the Northeast. My early favorite was Haverford, Swarthmore's sister school, and I really loved the place. My number 2 was Wesleyan in Connecticut, and I also gave Trinity a look. However, I met the same issues that have been mentioned here. My family qualified for a bit of need aid, but not nearly enough for us to be able to afford going to each school. Calling each financial aid office got us a little more, but still not close to enough. Several even conceded that they had no idea how someone with our income could contribute what was expected, but the decision was out of the speaker's hands.
You don't have to forget the idea of attending an LAC, though. There are great LACs, especially outside of the Northeast, that do give merit aid and are much less formula based with their aid. As many know here, I'm attending Rhodes College in Memphis, TN where I received a great merit award that made college an experience that didn't come along with debt. While I'm open to responding to PMs and forum posts about Rhodes, I'll leave my self promotion at that. There are many other great schools that similarly offer merit aid. Some that I experienced were Grinnell, Illinois Wesleyan, and Washington and Lee. Here's a thread at College Confidential where an attempt was made to list schools that gave generous merit aid -
LINK. The beginning of the thread has some outdated info (what stuck out to me was the mention of UChicago, who no longer gives out merit aid to undergrads) but overall it is a great resource and is kept updated and might help you look at schools that can help your son get things paid for.