HRR216K9VKA horrible on hill. Need knobby tires

I have a HRR216K9VKAA self-propelled mower that replaced an older Honda that bit the dust. I have a side hill about 100' x 20' (high) whose slope is at least 30 degrees. My old Honda which only had two drive speeds (low and high) did fine on low speed with the rougher stock wheels. However, my new Honda has a lever/paddle speed control which, a the point it first activates the wheels is already too fast. In addition, the hard plastic wheels are sooooo bad that even when stopped, the mower some times slides sideways. I've checked for replacement wheels, but they are all OEM parts. Does anyone know of any non-slip, knobby, all-terrain wheels that will work? Honda sells just the wheel (no tire) but I don't know if there are tires other than from Honda that would fit. Even thought of chains, but they all seem to be for lawn tractors. Any suggestions would be greatly appreciated (other than buy a new mower).

I have a dumb question.

Are you trying to mow up the hill?

On steep hills, I always hit 'em "lengthwise," with me walking slightly below the level of the mower, and the mower basically fishtailing (angled up/more or less diagonal) on the slope.

I let the self-propel do its thing, fast or slow. The forward speed is essentially controlled by the angle of the mower relative to the hillside. Also, I don't have to worry about mowing straight up or straight down the hill.

I realize your treads aren't as good as the ones on your previous mower, but unless it's super wet on the hill, my method should still be workable for you?

No, I'm mowing lengthwise. The tires just won't grip and I've had the mower actually slide sideways when you try to engage the wheels as they just break loose. I too walk below the mower with it pointed uphill a bit. There are two problems. First, the mower seems to first engage the wheels with too much speed so they try to break loose. Second, the wheels have just too little traction, hence my message. Thanks for the reply. You're the first. Hopefully, someone will have a solution.