Not very optimistic remarks so far !
Some various thoughts:
Would Spring/Summer flooding be more effective than Winter flooding (!???) - I have clients with an old punctured membrane pond which still stays quite "boggy" all year round; I have to deal with a few nettles around the margin, but no invasion of nettle or bramble etc into the boggy bits after several years of membrane failure;
If not interested in re-planting anytime soon, maybe add a good load of vinegar and, if desparate, salt as well (both will obviously wash out eventually);
And, of course, weed membrane will help while also keeping the foxes and doggie happy !!;
And just keeping at it, very very frequently, with a strimmer or burner or similar will EVENTUALLY work as well.
So, I don't really have a clear answer
Try everything and double/triple/quadruple up methods to whatever extent possible is all that I can suggest (if you are adamant that no commercial herbicides will be used on your land - ever)