Thanks for all the fine ideas! Here's what I finally did:
I seem to recall from last time I removed a sticker by scraping it off with a razor that the adhesive remaining on the windshield was water soluble. So I sprayed the back of the current sticker with Windex (which is largely water) and let it sit for a bit. Then I carefully scraped the sticker with a razor held as flat as possible against the glass, starting at a corner. I did a little at a time and it began coming off nicely.
When I had a fairly sizeable corner turned up I tried pulling the rest off, but that was a mistake because the corner broke off in my fingers. So I wetted the sticker again and went back to careful scraping. Eventually I got the whole thing off almost intact and with the serial number clearly showing.
Because the adhesive is on the front of the sticker, I carefully put a piece of Saran wrap on the front to hold the sticker together.
So, thanks again.
-Len