I think there is a species of butterfly that uses hops as a host plant for its caterpillars. If you can find some caterpillars, maybe you can control the hops that way. Just an idea...

I had hops along a fence at my former house (It was built during prohibition and they were making beer) and they were almost impossible to control. We kept trying to dig them out but they always came back from the roots. It did keep them from covering the garage. You might try digging out part of the vine if you want to keep some of it.

Pick and eat the young shoots as asparagus.

This is not good. I planted a seed not knowing what it was and it turned out to be a hops vine. It is growing over a lilac and into a Dawn Redwood tree. Great, now I'm going to have that and the trumpet vines that I can't get rid of. lol
Karyn

I feel your pain, Karyn.

Hops is a vigorous grower. My plants have climbed to the top of my 2-story house. But... they have also spread into the flower boxes, the AC unit, under the siding; have gone under the fence into the neighbor's yard...

Someone suggested eating the new growth. I could feed 2 countrys' armies.

I will dig it up ruthlessly this fall.