Sounds like spraying is the option. The nice thing about modern weedkillers is they want to be sprayed on the leaves - which you have access to. Think I'd do that first and see how it copes. And find a pole with a hook (or a hoe or whatever) to try and pull as much out/off as possible once it's dying. It's possible this might be a repeat procedure if you can't treat all of it but far less often than just trimming every couple of weeks. Maybe once or twice a year.