I've had mixed results with both superglue and epoxy. They'll stick some plastics really well but on others (notably polyethylene) they're rubbish.
+1. I have also tried Loctite's special
"ALL PLASTICS" (i.e. including polyethylene or polypropylene) superglue. £X for not much more than a pea sized dollop. A wee bit better than normal superglue (which is useless - well what do you expect when such plastic is used for the glue's reuseable cap?), but I certainly wouldn't rely on it holding anything valuable. Also that aktivator pen won't let you get into a crack/gap.
I can see superglue soaked fabric can be useful as reinforcement, but that is not the same as a good bond, if a good bond is essential. If reinforcement works given it is a bar mount is it possible to use/modify a Jubilee clip?
During my search for a good glue for those plastics (and which was not successful), someone somewhere said anybody who discovers a strong, simple glue for those two plastics would become a billionaire overnight.