Dont know your local politics out there, but I would likely just not mow it since it couldnt be done safely.

My first question would be if it is a ditch why does it need to be mowed.
Secondly.... how can they say it is the landowners' responsibility when the township has the right-away for a certain amount of feet from the center of the road.
If they don't want to mow it and I don't care to I would just let it go.

I have been trying to rehab a JD sickle bar mower for past year. For some reason, parts sold today.........specifically the guards on the sickle bar.......don't fit. Sickle sections will not register on the guards so it won't cut anything. Guards have same part number, but don't fit or work. Shame as it would be used for same purpose as OP has in mind. It has a 9' reach and will handle slopes up to nearly vertical or down about 45 degrees. It is a pull type and belt driven. As is, also a pile of useless unk.

Modern era replacement used by county road crews is a very expensive 100+hp special purpose tractor with an offset rotary cutter on hydraulic arm boom..........blades turned by hydraulic motor. Think of it like a side mounted excavator arm........tractor stays on road, the boom arm follows slope of adjacent ditches. Will also rotate to vertical to lop off limbs above fence lines. Works for government as they have unlimited budgets to buy such toys. Perhaps somebody who has one of those could be hired to do it?