I rewrite it, my head full of my own, original, new ideas. The results turn out great. There's a few if and while loops that look the same, and some public interfaces stayed the same. But all the guts are brand new, shiny, my own.
Do I have no rights to this code?
But code that is any kind of derivative of code before it contains a complex mix of other peoples rights. It can be relicensed, but only if all authors large and small agree to the terms.
I understand you need to publish the source code of your modifications, if you distribute them outside of your company.
What if I decide to make a JS or Rust implementation of this project and use it as inspiration? Does that mean I'm no longer doing a "clean room" implementation and my project is contaminated by LGPL too?
Generally relicensing is done in good faith for a good reason, so pretty much everyone ok's it.
Trickiness can turn up when code contributors aren't contactable (ie dead, missing, etc), and I'm unsure of the legally sound approach to that.
If they're dead and their estate doesn't care, you might pirate it without getting sued, but any recipient of the new work would be just as liable as you are, and they'd know that, so I probably wouldn't risk it.
