I'm 6'2" and rode a 20" Trek 7300. It always felt cramped to me. I got a 60 cm 4.5 Madone and replaced the 110 mm 7 degree stem with a 90mm 8 degree stem. I'm fairly flexible and I like the stretched out feeling especially on long rides. One thing you could do is get an adjustable stem and and slowly lower/move handlebars foward as your core strength improves.
http://www.nashbar.com/bikes/Product...3_10000_202442 is an example.