On anything but tight equipment, I suspect there are twenty candidates to break Mosconi's record, which is not really the record at all. I am among many that is quite certain that Mike Eufemia ran well over 600 and more than a few have attested to Babe Cranfeld having run over 700 in practice....twice!
OldHasBeen has posted about having seen the 4 x 8 on which Mosconi's run was made, and said [the pockets were so big, that the most impressive thing is that Willie never scratched].
On loose equipment, I believe Thorsten Hohmann, whom I believe to be the premier straight pool player in the world (though Tony Robles and John Schmidt could surely both give him a serious run for his money even in a long race). Thorsten, in my view, is the best straight pooler since Sigel and could run over 1,000 on easy equipment if he really wanted to.
On 4 1/2 inch equipment, however, I feel strongly that no player alive could break Mosconi's record. The three guys I suspect would be the top candidates would by Hohmann, Sigel, and Varner, but I just can't imagine a 500 ball run on a tight 4 1/2 x 9, even from these superhuman straight poolers.
And if we're using 4 1/4 inch pockets, even 300 is pretty hard to imagine.