And I turned up the gain on the low profile of the TJ Deluxe 64 Reverb, added a pure boost.
I took a quick listen to all the clips you've posted.
This sounds pretty close to my ears, though it's not quite right - it would absolutely fly for a gig.
I think you're goosing the gain a bit too much though - and while the amp feel/body sounds pretty similar, I think the difference between this and the live clip is probably more related to the cab/mic being used in this profile. Try using this profile, pull the gain back a bit, lock the amp settings, and try scrolling through different cabs to see if anything else gets you closer.
Try a compressor before the amp, and then try it after the amp stack, and see if either of those locations help out. Don't squash it too much - low intensity and squash, high attack, mix maybe somewhere between 60-80% wet. If you have the attack too fast, it's going to strangle that "thwack" you're trying to emphasize.
And... with all the good intentions and love in my heart, please make use of the great tuner that is available on the Kemper. You've got some nasty tuning skronk going on.