I may not know a whole lot about arrow building, especially where point weight affects apparent spine, but 160 gr for a point seems a bit excessive for a shaft spined at 60-64 lbs... You say the bow you were using is rated at 51#@27", and the shaft was cut at 28.5" as well. That means the shaft was actually bending quite a bit because of that 160 gr point.
See, the bowstring was forcing the shaft to move forward, but the weight out front of the shaft was forcing the shaft to stay put -- and the shaft had to go somewhere, and it seems to have chosen to go sideways, right into your hand. And has been said already: the fact that your shafts hit "sideways" on the target and several broke on impact says that something else is out of whack.
By the way, Killdeer, I have seen woodies break on release without first being cracked; Cedar shafting, new-made and **gently** flexed prior to launch to check for cracks. They were under-spined for the bow/archer combination by at least 10 lbs; spine-checked the "survivors" when the first one broke. The shaft has to be able to withstand the bending forces of "Archer's Paradox"; it doesn't have to be cracked to break apart on release, it only has to be too weak -- otherwise a shaft/point combination spined at 40# would be usable in a bow rated at 60#, even when that bow has a center-cut shelf. But you already knew that, I must assume.