I am 6'4". I have been on the following and they should suit a 6'2" person:
A Douglas 32 was way under for me, but might work in a squeak for you.
Some of the Grampians are tall I have read, but likely make other sacrifices.
Oh a broker was going to show me a Ticon 30, but it wasn't available that day.
I was on a Corbin 39 that was probably 6"2" to 6"3". These are mostly custom interiors so one likely would need to step onto every candidate to know for sure.
The best boat I have been on for me in the lower 30s is likely the Aloha 34, but I am concentrating my search on the 40 to 45 foot range now.