Can relate to you massively on this. I found my solution to be an IR loader (obviously still need the distortion pedal and really you do still want the blend on it), or at least for picking my sound for live use.
So I recently got a Darkglass Element and it’s been an absolute revelation. I spent a while finding an IR and eq that gave me the sound I try and get out of preamp (which is just me rolling quite a lot of highs) and I’ve ended up with 2-3 settings where the “clean” sounds pretty much the same across all of them but any distortion is wildly different depending on how much high the cab is allow.
So this would be my first recommendation, I think the Element is incredible, I now own two and it’s my di, IEM mixer, IR loader, eq, practice headphone rig, etc etc, so using something like that to dial in the sound at home through headphones. Then I would look at something like the Kasleder Albatross, Lusithand Ground and Pound or Backburner Big Booty Judy
https://kaslederfx.com/albatross/
https://bassbros.co.uk/product/lusithand-alma-comp-mkii/ - Though you may want the newer model
https://backburnernoise.com/products/big-booty-judy
The latter two are both rat clones, which I’ve really started to appreciate in the mix with my JHS Punchline, but it has to have the clean blend and it has to run into some sort of cab simulation for me to dial it in.