The Koren equations are the only thing I've found.

"Improved vacuum tube models for SPICE simulations" https://normankoren.com/Audio/Tubemodspice_article.html

The intractability of the Triode is part of the reason why the Pentode exists. And, you will note, the Pentode curves in certain modes looks a lot like your bog standard MOSFET.

This also discusses how the "constants" ... well, aren't. https://www.john-a-harper.com/tubes201/

That’s exactly what I’m looking for! Thank you very much!