I blow allot in the winter with my 2360, especially this year. The driveway that I plow is paved but has many dips and uneven slopes, not to mention it is a 12%, north facing grade. I don't have a BH on my 2300 but I rarely have trouble with the front end not going where I want. In fact, most of the time I blow in 2WD unless I can't get traction blowing on the upgrade.
I would guess the weight of the BH is undermining your steering ability quit a bit. As well, when I blow, I scrap right down to the pavement. I try not to leave any layer of snow behind that will turn to ice. And, make sure you have the hydraulic controller in the 'float ' position so the blower can move up and down with the surface, not the tractor.
DEWFPO