Naturally, not long after my last post I found this site listing out hitting streak records. It's not team-by-team, but you may find it helpful DCH:
Baseball-Almanac.com: Consecutive Hitting Streak Chart.
So, Jerome Walton does indeed hold the
modern-day Cubs record for a hitting streak at 30 games. But prior to 1900, two Chicago National Leaguers had equal or greater streaks: Cal McVey's 30-game streak in 1876 and Bill Dahlen's 42-game streak in 1894. Not sure if you're keeping pre-1900 records, but there it is.
P.S. Who is this DiMaggio fellow with a 56-game streak in 1941? Can that possibly be correct?