I can't speak for the classic, but there were some screws hidden beneath the analog board assembly. It may be possible to remove them with a super log phillips, but I don't think you'd be able to get around the flyback and capacitors with one. This was my first time, so maybe I'm totally wrong. I followed the Apple documentation and it was fairly easy to remove the 3 main internal components once they were disconnected from each other.
Unrelated: My SE/30 has a 250mb hard drive which was clearly an upgrade from the original. I had originally thought the HDD activity light was broken, but it turns out it was never even connected. Does the light connect to non-stock hard drives? I see two connectors (one 2-pin and one 4-pin) but neither are large enough for the SE/30 HDD light.
It's an "Apple Computer, Inc. Internal 3.5 Inch HDD 250MB SCSI / Firmware ©1993"