It took two cleaning sessions, but I got my wheel looking "presentable." I think my corrosion was deeper than some of yours, and it took more than just polish to get it out.
When I went to the dealer last week they were very helpful. The service manager and 3 or 4 of the mechanics all took their best shots at a fix for the corrosion. One guy recommended "clay bar." I've seen clay bar in the auto parts section, and it seems to be a product to restore the gloss to oxidized paint. Probably not effective on oxidized aluminum alloy. Another guy had some Aluminum Jelly, which is Naval Jelly for aluminum. We smeared it on the wheel and waited the suggested 5 minutes before wiping it off. It was ineffective, except that it left a whitish blemish. I don't recommend it. We tried some very fine steel wool, but that just scratched.
The service manager said that he once had a BMW with the same sort of wheel rot. He spent a Sunday afternoon working his wheels with Simichrome and had excellent results.
I gave him my info and he filed a claim with Triumph.
I got a tube of Simichrome and tried it out. It was about equal to the Mother's Aluminum Polish that I already had tried. It made the wheel shine, but didn't dig deeply enough to remove the spots. So I decided to get tough.
I went to the kitchen and found the bottle of Soft Scrub. Soft Scrub, if you don't know, is a mild version of Comet or Ajax. It is for cleaning fiberglass bathtubs and plastic sinks without scratching.
On my wheel, Soft Scrub was very effective. It was abrasive enough to penetrate the top layer of metal and dig down to remove the spots. Unfortunately, it left the wheel dull. But a couple of applications of Simichrome brought the shine back.
I may have to do one more application of Simichrome or Mother's to get it back to new condition, but I am pretty pleased with the results.
Here are the before and after.