Hi Max, also here is another solution for you - the attached version should be able to chamfer those edges ok for you now.

In this version I have reconstructed the narrow strip to be just one long single surface rather than being made up of many different surface pieces. This significantly simplifies fillets and chamfers since they won't have the same kind of juncture problems as on your original surface.

To get the strip as a single surface, I deleted the existing strip, selected naked edges and ran Edit > Join to get 2 long closed curves. Then I ran Rebuild with a tolerance of 0.001 on those curves to make a new version that was fused into one single simple curve rather than having separate segments in it.

Then with the fused curve I did a loft between them to make a new single strip surface, and relocated the seam points in loft to a perp/perp line that I had drawn in at the top.

With this simplified object structure with less fragmented surfaces you should be able to chamfer it ok now.

- Michael