Had the same issues with my 2010 Nytro [121]. Tried doolies, was not happy, in fact i found they made things worse - put a pair of Split Rails and havent looked back. They changed the sled entirely. Amazing the handling difference. No more push in the corners. In fact the worse the conditions are, ie rutted trails, deep tore up snow, the better they handle.
Pm me if you have any questions. Good luck
MS