I've been following this thread for awhile, and after several attempts have a great high score.
High Score: 2,948,751
Sponsor: Blue Sun
Commander Profile: Custom (so I could select breakthroughs, more on this below)
Map: 44N112W
Mystery: Dredger
Rules: Hunger, Rebel Yell, Chaos Theory, Winter is coming, Armageddon, Dust in the wind, Twister
Difficulty: 545%
Martian Copyrights: researched 1 time only
Endless Supply: no
Chaos Theory: yes
On Custom Commander Profile
Now as you can see I used a custom commander profile. Let me explain. If you actually want to compete for against the existing high score you need to export minerals and you
need to roll certain breakthroughs. I spent many hours (and days) re-rolling for the perfect sequence of breakthroughs but it did not happen and I eventually realized how silly it was to spend all this time re-rolling. So I made the custom profile and got on with the game. My profile simply made the breakthroughs available in an order of my choosing. They still needed to be researched. The first breakthrough starts at 1000, and they double in cost each time, quickly becoming 80,000 research points.
So you can dismiss this high score submission if you like, or maybe classify it under "custom command profile" but I actually think allowing players to choose the type and order of their breakthroughs could be quite invigorating for the challenge. I've already thought of quite a few new strategies that could top this score if I change my initial breakthrough order.
On Chaos Theory
I haven't seen anyone say it's illegal to use, but it's pretty broken. I'd suggest marking any score submissions that use it. And ultimately all it does is introduce a new re-roll vector to be competitive, so now you gotta re-roll breakthroughs and your chaos tech tree
Playthrough
I rolled early space elevator and trilobite scrubbers on chaos theory. Combined with the 1,2 slot Extractor AI & Core rare minerals I was able to setup efficient rare earth production extremely early. This setup an early space elevator which was complete around Sol 25. After this I expanded and mined all the rare core earth deposits (3) on the map. Most difficult problem was exporting all the rare earth, even with space elevator. The dredgers mystery was probably a bad choice as it shuts down the space elevator (disables the resupply tab) for about 10 sols, which really creates a backlog of rare earths that you can never ship.