I think this may have a lot to do with the fairly deep sidecut of the board. My Billy Goat is even "worse" for that on hardpack. It is even more of a turning machine. This loosy goosy feeling is pretty native to the C2 style of rocker/camber and why many east coast riders prefer the solid feel of traditional camber. By the way what is the camber profile of the Jones board you suggested? Just curious if this could be a factor.
You should check out the web site and look at the flagship as well. I have this board and it just rails on hard pack/ ice.
p.s. I am 55 so I understand not wanting to splatter on the trail