I think the only solution apart from Roundup/glyphosate is to cover the area with black polythene or carpet for a year or two (or three!!!)

If you strim it you cut it into many pieces, all of which will try to root!

i have found spraying roundup type weedkillers from september on quite effective. the weedkiller gets taken down into the underground storage parts. and then those sections die off over winter. I tend to spray 3 times beginning/mid/end september. as the plant is also getting ready for winter dormancy it will translocate the poison down.

I agree not to strim, you need the top growth to be there to take the spray down.....

Spray several lengths together put into a plastic bag tie it up and leave until dead. The weed killer needs to get to the roots to do the job. Good luck.
Brucem.