FWIW I have a JTM 45 1965 all original - It's one of those items that I will never sell... I cant replace it.
I have a IIXL (Im on the wait list for the III) In the past I tried to recreate the sound/tone and feel (feel is of major importance to me) The short of it is - I got close, close enough to get a smile (and that's important too
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The long of it is - It took an unbelievable amount of tampering A/B ing and lots of F***s & other expletives to get there, and many hours - Jeeze many hours. Its long gone now (the preset) But from memory I recall the IR being not so important, there were at least 3 or 4 factory cab options in the XL which worked well, I always use a PEQ block after the cab for any final tone shaping anyway, I sometimes also use one before the cab block too.
The real amp even in non jumper-ed mode has sooooo much bass and thud I usually need to turn this down to around 2.5, then almost max out mids and treble (a smidgen before full - or the magic is gone) Copying this in the axe did not have the desired effect. Im pretty confident in saying the bass needed to be absolute zero and the mids & treb needed to be maxed. So dont be afraid of maxing or minimizing the basic controls some models need it.
The output tubes where KT66's and I remember this being very important to change too.
Also in the dynamics page I needed to play with Dyn Presence, Dyn Depth, Preamp Dyn. Cant remember how, but basically the real amp has this glorious mids chirp to it when you dig in - The sound sonicaly laden with just the right frequencies which just jump off the fret board at will... This was very difficult to achieve but I got close. Supply sag also had a role to play (think that needed turning up from default) There were many other tiny tweeks to the deep parameters I think there was a Q value somewhere which needed adjusting (sorry I'm not in front of axe edit right now)
Overall I would say I got 80% there in terms of tone and 65% in terms of feel. I found you could get closer on tone but lost out in feel, or tweek to get closer on feel, but then lose out on tone.
It's a tough journey which can be fun or frustrating - Never in between for me, always one or the other each time I go after a sound.
One thing I had to bear in mind is that the amp that was modeled was not my actual amp to start with - so it was never going to sound like mine anyway.
From what I read and hear the Axe II had limitations and compromises needed to made in terms of amp modelling but the III has almost eradicated that problem, so hopefully you can get even closer. Im looking forward to getting my hands on the III and I'm going to try again.
Final shout - beware the firmware updates. If you do go deep into the parameter pages and tweek, and then finally find the sound you are going after, there is then a very, very good chance all your efforts will be gone in the blink of an eye, because the firmware will take that away and you need to start over. I've had my fingers burned too many times. And its the reason I dont have the preset now. Sometimes you cant really stay on the firmware because there may be a bug fix which you need, so you have to upgrade..