If I understand you the right way you are looking for a kind of distorted wave not depending on amplitude. This will not work imho, and if you measure real tube circuits, you will not find this either.
At some point the amplifying device will saturate and/or cutoff and flatten out the signal. With tubes it may be more "gradual", but not necessarily. For high gain tube amps there may be three stages of amplification in the preamp section, and all will contribute to the distortion. How much is actually hard clipping depends on the intent of the designers and also how the player uses/abuses the amp.
I was messing about with SRPP jfet gain stage and with a (gasp) diode in some local NFB managed to get a pretty good soft limiting on it. It does jiggle the biasing a bit on strong signal input peaks. Some further investigation to go, would like to set it up on multiple stages, but it's quiet and has decent gain.
Attachments
I think it sounds quite promising, and would like to get 2 stages going with a tone stack in between. It's quite subtle, like you probably wouldn't notice the limiting too much going into a tube amp, but into a solid state power amp it has some nice warm overtones. Definitely not sterile but not in-your-face distortion either. Cheers!