^^^^^ beat me to it!
Maybe find a 6002L bearing and try to use the seal from that? You could also have a machinist make you one out of a hunk of good brass with a bit of a lip to pop it in and out.
There are definitely ways around this, it's just a challenge and a puzzle.
(Second edit) One more thing, I have at least 12 old seals from 6202 bearings which I replaced on my wife's cargo trike. They are slightly thicker, as in the hole of the donut is smaller. You are welcome to play around with them if you like. I can grab them out of the garage and pop them in the mail, no problem. Bearings are pretty cheap on the site from the big river in South America, so I say buy a selection, get a hobby knife, and start gently prying.
Last idea is to have your seals 3d printed.
Phil