I think you would be O.K. at 62 grains. I think 1/9" is a fine twist for the average 223 shooter. Instead of hearsay I'd load some up & test them yourself.
I have two 16", 1/9 twist barrels and they handle the Winchester 64 PSP bullets very nicely...Just work up your loads for accuracy at 100 yards and you should find that the 62gr bullets work well out farther than 150 yards...
I shoot 69 gr SMK's out of my AR with good results. I shoot 69 gr SMK'S out of my LTR out to 600 yds with great results. 62 gr Green Tip Steel Penetrators shoot very good out of my AR.
77gr SMK stabilize in mine just fine, Velocity is a tad low to get to 1,000 as well as I'd like. But in my 24" Bolt gun(9-twist) they are perfectly fine.
There are ALWAYS exceptions, but both my 10FP and M4 like them.