You don’t need the serial number. The website asks for it, but will happily give you a value even if you leave it blank. Anyway, checking EE bonds $200 face value issued in January 1991 - 1997:
It turns out that Capital One and Chase will both cash up to $1000 worth of savings bonds for non-account holders, if you ask them nicely. And it didn’t take that long, either.
Good thing they did, too. I forgot how expensive Manhattan was.