I think "more power" and "more spin" are probably contradictory in this case. Most strings that significantly increase spin are going to be the same or even lower-powered. Most strings that add significant power are going to decrease spin over full-bed Lynx Tour.
I think Lynx Tour is a typical average poly string power-wise. I would call it medium powered for a poly with medium+ spin and a firm (but not harsh) feel. It's unlikely that you're going to get a huge power increase unless you go for a different string type altogether in the hybrid. But that will drop your spin by a lot.
Maybe you could consider a slippery round poly in the cross with a little more pop than Lynx Tour, something like Poly Tour Fire.
Or maybe you just need to play with reducing tension, especially on the crosses.