Bullet weight is not the only criteria that determines if the bullet will stabalize or not.
I know for a fact that the 25gr Hornady HP will stabablize just fine in a 1:12 17 caliber barrel, whereas the lighter 20gr V-Max design will not.
If the bullet is real light up front compared to it's length, like the polomer tipped bullets, you are going to need more twist than with a bullet that has it's weight set back, like a deep HP design with lots of empty jacket up front.
I have fired 60gr bullets with good success in 1:12 .223 barrels, so with the right design of a 62gr pill, it would probably work. Maybe a deep HP, rather than an FMJ.
Who here on this board would argue that a heavier bullet would stablize in a slower twist barrel, but a lighter bullet would not? It will take this group by surprise, but if you really want to discuss bullet design, this is not the site...... www.saubier.com would be a better choice.