C-, you know, I really envy those short armed guys that can shoot those nifty looking little jewels that are 56-60" long. But then, I really envy those squatty body little farts that can fit behind the wheel of a Corvette too. On the other hand, I don't need a ladder to reach the stuff on the top shelf.
In theory you could get a 62" bow to draw stack free if it has a short riser section that's got a pronounced deflex in the throat of the grip, long length of working limb and a deeply hooked working recurve. Like Wingbone said though, this is something you MUST discuss with the bowyer. Every bowyer I've approached so far has said I need to go longer. After they've gotten over the shock of disbelief, that is.

The Chek-Mate Kings Pawn I've got on order right now is 64", and that will make it the shortest custom recurve I've ever had. All the others have been 66-68".
If you can get a bow made that draws stack free to 32" (which you can, even though it might be longer than 62"), and if you're comfortable shooting 56 pounds, then order 56 pounds. 55 actually. Most bowyers will guarantee to hit weight within +/- 2 pounds and it's usually +. You'll see an amazing difference between shooting a real 56 pound draw vs a 48 pound draw that stacks to 56. The difference in smoothness of draw, definitely, but you'll see a very noticeable improvement in performance. Maybe even dramatic improvement.
Because of the stack, what you're shooting is a 56 pound bow that performs like a 48 pounder. The 8 pounds of stack does virtually NOTHING for you. Someone with a 29" draw can take your current bow and your arrows and shoot exactly the same speed as you do. That's what stack does for a long draw shooter.
Talk to the bowyers and see what they say. I'd bet you wind up with a 64" but you never know. Good luck.