Like they said, the straps stretching is probably most of the problem. I'm also 6'4", with that exact model of GTUL (same color, even).
I've been able to take short naps in it, but it's definitely not my go-to hammock to sleep overnight in. I usually just have it along for a quick-to-setup rest break when hiking. A longer and wider hammock will make a significant difference, comfort-wise, when you're ready to invest in it. If you're not ready to shell out the big dough yet, a Skeeter-Beeter Pro will have plenty of room for you, at about $60.00.
Another potential issue is that the trees are a bit far apart for that length of hammock. I've found that when I hang it from trees 15 or more feet apart, I have to tension it quite a bit just to not have it touch the ground when I initially get in (and I don't have straps that sag -- this is just with adding mass to the equation and the slight stretching of the hammock body itself) -- either that, or hang the straps really high (usually around 7 or 8 feet). I actually have better luck for comfort in it on my back porch, which has posts only about 12 feet apart. Try a shorter distance, with the straps hung about level with your eye or just above the top of your head -- this will give you a decent amount of sag.
For overnight sleeping times, though, I'd still suggest upgrading to something a little bigger.
"Can't we all just live in trees and hammocks?"
-- Sam Gribley, My Side of the Mountain