Your son seems pretty gung ho about Greek life, but you may want to reach out to the OP on this thread: Wake Forest sophomore looking to transfer-Match Me and Chance Me! [3.7 college GPA; history, English, government]. I don’t know if her son always planned to not go Greek, but at least this one individual seems to have had a hard time without an acceptance to a frat. I would investigate for any campus whether or not a student is essentially guaranteed a bid if they go through all the steps (i.e. filling all their slots with possibilities, etc…I didn’t go Greek, so I don’t know).
Another school that your son may want to consider is Samford. 35-40% of its males join a fraternity, it has about 3700 undergrads, and is probably within driving distance of most of Florida. This would be a safety. 56.6% of classes have fewer than 20 students and 2.3% have more than 50, per USNWR.
Georgia Tech would be a reach, but work hard, party hard seems like a good description of much of the student body. About 22% are in fraternities and Atlanta is likely within driving distance (and almost certainly a nonstop flight away from your nearest airport). Almost all Atlanta schools are part of a consortium whereby they can take classes at other schools (like Emory, SCAD, Spelman, etc), so he could also dabble at other schools, too. And its business school has a good reputation, but small classes at the university are not as common as you’d probably like (per USNWR, 29.5% of classes have more than 50 students).
Speaking of Atlanta schools that are part of the consortium, Morehouse could be an interesting possibility. It’s an all-men’s HBCU with about 20% of its undergrads joining a fraternity. There are about 2600 undergrads here, but with the ARCHE consortium (and very close relationship with Spelman, about 2400 undergrads), it definitely has opportunities to have a more expansive feel. 49.6% of classes have fewer than 20 students and only 0.7% of classes have more than 50 students, per USNWR.