Point is that tyres make only a minor difference to off road ability compared to diffs. By having better diffs with good road tyres you have a more capable car on road and more capable off road. Win win.
Both cars were turbos. Both cars were aired down. A welded diff would be as effective off road as a locker, until something broke. And a nightmare on road. Yes the SH made it up, more due to the driver than anything else. And not without cutting up the track even more.
I'd love to have a locked diff but I don't think you've proven your point about tyres. On the dry, loose surface you were on the tyre compound would be more significant than the tread pattern. What you need is two cars, identical bar for different tyres to do the same run. Then you would have a valid comparison of tyres.
I would be very surprised if your road tyres would get you the same distance as KO2 tyres uphill in muddy conditions given all other things were equal.
In most dry circumstances in Australia tread pattern makes only a small amount of difference. On sand, there is no doubt that road tyres work better. The true advantage of AT tyres is in their construction and the benefits that offers in rough conditions.
Firstly, additional sidewall strength reduces the risk of damage from sharp rocks, roots etc. I have personal experience of tearing a great chunk out of the sidewall of a road tyre while competing in a rally. An instant flat is the result and that's the last thing you want on a steep climb. It's often very difficult to get the car somewhere a wheel can be changed when one tyre is flat. Having it happen at speed is another story.
Secondly, most people who fit AT tyres go for a higher profile that allows running greatly reduced pressures without losing so much ground clearance as with standard road tyres.
Thirdly, but not last by any means is the ability to run AT tyres at reduced pressure for extended periods of time with less risk of overheating the sidewalls resulting in tyre failure.
I do some beach driving and some bush driving. Although road tyres would work as well, or better on the sand for short runs, They have distinct advantages on other terrain or over long distances at low pressure. In my opinion, a set of good AT tyres is a much more practical investment than a locker in the first instance. ( I still want a locker, but AT tyres come first because I can afford them and they don't cost more than my car is worth)