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I have been trying to do this for the last sixteen years.
After years and years of trying, I finally reclaimed the world championship of Timeshock! and topped Tarek Oberdieck's old record with 80,582,604,780. This is recorded on Andreas Grabher's high score leaderboard.
I rebuilt a DOS machine for Timeshock, with my good old Celeron slot-1 motherboard, a real Timeshock CD in the drive, and complete with my trusty 15 year old Gravis Ultrasound for sound. The DOS version performed perfectly. I rolled the Super Jets total over 2.1 billion (2^31) fairly early in the game and no crashes at all.
Like my 75B game a year ago, I did it mostly by ignoring the explorations and just playing Time Machine Frenzy. I went to Dawn of Time and End of Time only twice. Mostly I just traveled back and forth between Present and Ancient Rome in order to repeatedly collect the quickshot souvenir parts for Ultra Magnosave (Magnet and Tyrian Toga.)
The game was going well, ahead of pace. Tarek's score of 78 billion in 13 balls works out to exactly 6 billion points per ball needed. I had 55 billion on ball 7... but then drained three times quickly, twice while trying to complete the Volcano exploration. (That was the only time the whole game that I lost without holding the bonus X and Super Jets totals.) Then later my second-to-last ball drained with about 68B on the scoreboard. So close.
One ball left to score ten billion points. I had also lost Ultra/Super Magnosave, but fortunately the Super Scanner awarded a Super Magnosave on the last ball right away. So I carefully shot for nothing but Time Machine Frenzy over and over again, staying in Ancient Rome (that's better than Present, since the souvenir pair gives Ultra Ball Saver, better than Very Big Points.) My heart was pounding, palms sweating, and I did very badly for a few TMFs, but then recovered and nailed two Ultra Jackpots in one TMF to jump from 72B to 74B. A few more TMFs finished the scoring, with the record-breaking point coming on a Super Jackpot. My last TMF didn't score an Ultra Jackpot but scored over 1B from lots of regular and super jackpots to climb over 80 billion.
The game ended draining down the middle, on trying to catch the ball for a quickshot (even while just shooting for TMF, it's worthwhile to clear out the quickshots every now and then in order to refresh the lucrative left orbit awards of video mode - super time warp - reverse frenzy.) But I am satisfied.
Final statistics: