Physically- Im pretty sure that that defies the laws of physics. The only factor that could be causing the arrow to apparantly speed up in flight is wind, on the other hand, wind/air and gravity slow it down/act against its flight. Unless you have little rockets on the end of your arrow im not sure how this could happen
The only REAL theory I can think of (and its way out there) is that your arrow is FAR too weak thus creating a wobble that eventually is cured by the fletching @ 30yds, and then the arrow stabilizes (gets straight again) and picks up speed. The whole "nodes" thing is really the only thing that comes to mind. If your alignment is out of whack b/c of weakness, and all of the sudden, they align, maybe it could gain speed???
Like i said, way out there. And you said for yourself that you can get bh's to hit with fp's so i would venture to say that your spine is correct as well?
Derek