I haven't a clue how the big names do it, I'd imagine there's a significant bit of free solo while trailing a rope, with the ability to set up a self belay when things get too crazy. Sort of like soloing the NR of Stuart, and wanting to rope solo the Gendarme pitches, just many notches in difficulty and seriousness higher. Traditional fully self belayed solo, like folks do on El Cap, seems much too slow to apply to big mountains where the "speed is safety" cliche largely holds true. I'd imagine your big alpine self belay system would need to be simple, light, and somewhat functional in storm, so fancy dan devices are probably not the ticket.
If you do something like this, be sure and take pictures of your feet and post them here.