You could buy yourself a scythe, it would take about 3 hours work to do a quarter acre with one but you will have to remove the cut material before you mow otherwise it will still be too much for the mower just as the whipped stuff is now.

Go to a tool rental shop and rent a tractor with brush hog

I have no lawn; I live in an HOA and discussed the benefits of my native habitat with it. I have no problem anymore. See my FB page for photos as they are public

I'm no help, your neighbor sucks, it's beautiful! I say maybe ask for help, barter? I would help you for Milkweed seeds.

I only trimmed the grass when it started to tickle my knees. One year we had a plague of army moths - they would fly up from my straggly brown overgrown landscape and invade the neighbours pristine mowed and watered twice a week lawn where they would lay their eggs. On hatching the caterpillars would eat their way down to the roots leaving lovely random brown dead grass trails through his lawn to create a lovely contrasting pattern....

Can you keep some Milkweed in your gardens?

A bush hog should do the job and if that doesn't work then a jerry can of gas and a match will, just make sure the wind is blowing towards your neighbour.

Have you looked into fighting the decision? There has to be an appeal process.

1/4 acre isn't much. Hire a lawn service for one cutting. Should cost about 40.00.

If it’s fenced in borrow a few smelly goats that will make your neighbors happy.