Simsportplyr, I have two different Weber SS pans that I've been using for several months now. I've tried most of the recommendations you got (Bar Keepers Friend, steel wool, etc) but have yet to get either pan as clean as I'd like. I try to get the most of the carbon off, but am resigned that I'll never be able to get rid of the discoloration.
Migrating the discussion back to the correct sub-forum.
Doctor Weber (!!),
I tried a thick baking soda paste (soda-water) this afternoon, leaving it on the black parts for half an hour or more. Then, I scrubbed with a plastic scrubby, got nowhere.
Then, I tried a (less thick) vinegar-baking soda mix, and that didn't work, either.
I have successfully used a vinegar-baking soda mix to eliminate charred stuff (usually, burnt sugar) on saucepans before, but I was able to heat up the vinegar-soda mix. Due to the large size of the grill pan it is non-trivial to heat it up and scrub, and I'm sure that the lack of heat reduced the effectiveness of the vinegar-soda mix.
I recalled that one of you kettle-masters suggested using a razor blade, so I got out an old steak knife and within a couple minutes was able to remove all of the significant remaining black sections on top of the pan. It was a heckofalot easier than scrubbing.
So, now I would say that the grill pan is clean enough for my sensibilities.
In the future, I think that a mix of BKF and scraping will do the trick without excessive effort. I'll also try an oil with a much higher smoke point, like peanut.
Thanks everyone for your helpful suggestions! Without you I probably would have given up on grilling and taking up drinking!