We’re from NYS and our EFC was 1/10th of what yours is, but our son’s stats were similar to your son’s. Penn State’s net cost was ~$40k/year, so I wouldn’t expect any aid there. I think most of the other colleges on his list will be outside your budget too.
Driving the process is fine as long as a student can do that within the parameters set by their parents. I’d run the net price calculator on each college website and remove any college from his list that comes back over budget. Better to be firm about the budget now than to have to toss out offers in the spring. If he really doesn’t want to go to Buffalo, he’ll develop a liking for something else.
Some kids see the EFC and think their parents can pay, and when parents allow the apps to go to the “unaffordable” colleges it just reinforces that, so they often feel blindsided in the spring when parents refuse to pay and they end up at the safety they never intended to attend (which means it wasn’t really a safety at all). You need to provide some firm guidance so the options he has in the spring are some everyone can live with.