I've had similar spots on my window weatherstrips, too. Like you, I tried a lot of different things to remove them. What I finally found was that a little "bite" was needed to exfoliate what I think is dead rubber. I used a green Scotch-brite type scrubbing pad and 3M Adhesive and Wax Remover (rubbing alcohol may also work well, as it's good to remove dead rubber from wiper blades). I went sparingly with the 3M stuff, and used the pad fairly gently. I kept another clean towel in my other hand to wipe the weatherstrip as I went along (as much to remove the exfoliated "gunk" as to prevent the 3M adhesive remover from dwelling too long or running down my paint). I found that several passes doing this worked pretty well. Afterwards, you can apply your favorite dressing. Yours appear faded like mine did, so I used Forever Black to restore the black appearance. Mine look 10x better, and the Forever Black has held up for probably atleast 5-6 months.
Hope this helps.
Dave