I was in a similar situation, a space between my neighbors wooden fence and my chain link fence was always infested with weeds and looked awful no matter what I did. I ended up planting Carex Ice Dancer along the fenceline and let nature take its course. Now, two years later it doesn't have complete control yet but the whole area looks much nicer. I say go for it.

Yes, you can fight awful weeds with less awful weeds. I have found Teasel to not be that hard to fight, I whack off the flower stalks, in 2 years, almost none re-appeared. Looserife is much harder, I sympathize with you.

If the ditch lilies don't do it, maybe a short bamboo? Bamboos will not cross flowing water. I wouldn't recommend Fargesia, but there are short bamboos (Rice Bamboo, for instance, if it is hardy).

If there is room, maybe Pawpaws? If the ground is not soggy, they will grow and spread by underground roots, making a nice grove of low growing trees that shade out everything beneath.

Jeanne's suggestion of ornamental grasses/sedges is another consideration. Good luck with your battle.