Load-Range, Sidewalls, etc.
As you noted, new or newish tires make a big difference. Comparing well worn treads to new tires with deep tread is like comparing apples & oranges.
Aspect Ratios
I did own a 2005 LJ and ran 245/75, 265/75, 285/75, but mostly 255/85R16 tires on the Jeep. Like you, I also prefer something less than a LR E tire for ride and flexibility (performance/traction). The traditional load-range of a 255/85 is "D", which is perfect in my opinion for most utility vehicles focused on overland travel. The Toyo M/T is truly stiff, but the KM2 is remarkably flexible and rides well for a LR E tire. I'm not trying to push you to the KM2, just being fair, the tire does have some attributes.
Part of the reason the stock 245s on your Wrangler are firm is not only because they are a LR E, but also because of the limited sidewall height. Though they have an aspect ratio of 75 (assuming you have 245/75R16?), the total height of the sidewall is quite low and therefore doesn't absorb shock as well as one that’s physically taller. I have noted this many times when testing 245/75, 265/75, 285/75, 255/85 tires. I started to really take note of this when I had a set of Toyo M/T tires in both 285/75 & 265/75 mounted and balanced on two sets of stock wheels for my LJ. Same tire, both newish with most of the tread remaining, run with the same PSI, but the 285s rode softer over little bumps in the road. Neither was soft or forgiving, and since you like a less firm ride I too would steer clear of the Toyo M/T.
Which Tire
I really like the Maxxis Bighorn, I've owned two sets and they have all balanced well for such a heavy truck tire (heavy for a 255/85). In fact the excellent balancing pushed me to buy and try a set of Maxxis Bravo A/Ts, which also balanced well. With most of your miles on-highway (like most of us) I really think you should consider something that will wear longer than a Bighorn if that's at all important to you. I haven't run KM2s long enough to collect wear data, but treated similarly I think they will wear longer than Bighorns.
The above mentioned Bravo A/T (Bravo thread) will be a much quieter, better wearing tire, but it's also not even close to an M/T, not even an A/T. The Cooper S/T or the Dean SXT M/T (same tire) is possibly a very good choice for a nice void ratio with good wear potential. They are LR D and they ride nice too. There are lots of picture posted here on The Portal comparing the different treads of a few 255/85 tires, but you need to see the Cooper S/T in person to decide if they are the right tire for you.