I know it isn't "the most" but in 2009 Oliver Ortmann ran 100 and out in the final two matches of the preliminary round and followed that with a 150 and out vs Earl Herring. 3 consecutive matches for a total of 350 and out.
The Herring match is on an accustats video with Ortmann doing commentary.
Here's a thread about that feat: http://forums.azbilliards.com/showthread.php?t=154499