Last couple of clips added.
I used the custom learning rate values provided above - these got the ESR way down to 0.0037 for the example without the Ampete, and 0.008 for the version with. I think clip H gets the closest to the source tone. I can still hear some differences but it's the closest so far to getting the distinctive characteristic of the amplifier correct. The low end is still not quite there, and the real amp feels a hair smoother and less abrasive.
Thanks to all those who helped with the tweaks - starting at 0.01 and ending at 0.0037 is good going.
IMO capturing tech should be as close as it possibly can to the source, so I applaud those pushing boundaries on making that accessible to others. I'll definitely be using these tweaks going forward, the differences might be small but they're often in very important parts of the tone. Even though all those clips sound passable and good enough, many of them feel like a slightly different amp to me (if Im expecting that huge low end to punch through). I think this all just makes me want to use real amps even more on projects, all kinds of modelling are awesome for what they are but there's some magic when you turn an amp on and dial a tone in. You just get THERE faster and you have something distinct with personality at the end of it.