Like the mighty cat of cankles, I have 48/38/28 with a 14-34 on my grocery/tour bike. and yes, there are some huge leaps. You Need a triple with that cluster. Unlike the OP, I don't regularly cruise at 24.2 mph (90 rpm in 48x24.) If he can do that without tapping his legs .... I am wondering how he tracks his speed, and I am wondering what cadence he rides .... and a lot of stuff .... cruising at 20 mph and above and he only rides 20 miles, once a week." Is he a weightlifter or a 440-yard sprinter the rest of the week? Not if he runs out of wind.
The easiest answer is to simply shop online for a 7-speed freewheel with better gearing,. If his bike is new he shouldn't even need to change his chain .... not sufficiently worn yet, I;'d imagine, to damage the new cluster.
His other option is a new crankset---and again, he can use the same rest of the drive train.
A better ides would be to get a new rear wheel with a freehub and cassette.
The best idea is to look into competitive cycling if he can cruise for 20 miles at 20 mph without his legs getting tired at all.