Huh! Somehow I managed not to notice the Angel Tower / GojiTail thing, even though I'm the one who added most of the stuff about the former to the wiki!
That's really nifty.
The "swerving light beam" can probably be traced back at least as far as the God Warriors from the Nausicaa
manga. Anno himself animated the melting, somewhat less lively one in the animated film, but you can see them destroying stuff in all their towering, toothy glory in the "God Warriors Attacks Tokyo" tokusatsu short by Anno and Shinji Higuchi, narrated by none other than Megumi Hayashibara.