That picture is about a 5 or 6 on a steepness scale of 1 to 10 on the driveways I plow on the mountain for my customers . Go with a set of chains .... my New Holland tc40da has the same problem with the R-4's , just a little ice and it's all over ,chains are night and day difference.
If your driveway is the only one you plow and you do not want to buy chains try throwing some sand or salt or pea gravel down for some traction getting back up a few shovel fulls make a big difference.
I cover a pretty good distance plowing from one to the next and hate the chains over the road for any distance and found keeping a few garbage cans at the half way point on the steep driveways and flinging a few shovel fulls of salt,sand mix is all I need to get the job done unless it is pure ice. Good luck and be safe .