I said I'd post instructions on this, and so I will. (I wasn't able to post for ages -- hence the delay.)
It's a really simple thing to do, so here goes.
1a. Go to your local Honda dealer and pay $50 for a new lower window moulding.
1b. My moulding came with the seven moulding holders and screws. You might want to check that this is the same in America, since two of my original holders cracked when I removed them, simply due to age.
2a. Remove the lower window moulding. There's a trick to this. It sounds a bit weird, but you just have to have faith.
2b. For each holder, unscrew the screw fully. Then, press the screw back in as far as it will go. (Just push -- no screwing action required.) This action presses on the internal clip mechanism, and you should then be able to pull that holder straight out (if it hasn't disintegrated, like my two did) (although it's easier to do all seven first, then pull on the entire moulding).
3a. Put your new moulding into position, checking the position of each of the seven holders.
3b. Screw in each of the seven screws.
4. Marvel at the beauty of your new, rust-free window moulding.
I think this is worth doing. It appears that the design of the piece has changed since the original (I guess Honda noticed the flaw), since the new part I got was plastic, rather than the apparent painted surface of the old part.
Here's the car with the moulding removed:
And here's the finished product: