Going off of SF=2000, this would likely be (in-universe) as the 2009 season (9 ASF), where the Cubs still almost took the division title. (I know Jim wrote it in '08, but chronologically it fits anywhere in '07-'09 (all decent seasons for the Cubs).
Zambrano has pitched for the Cubs since 2001. More importantly, from Curses, Harry thinks Tampa might have a chance. This puts 2008, 2009 as pretty likely, as Tampa didn't really start looking good until then. hat he thought them a threat to the Yankees for a postseason title...well. He'd had to have seen them pull off a good run at least once (as in 2008) to take them seriously.
Also, Harry called them Tampa Bay-- but he called everything else by team name (Cubs, Yankees, Phillies)-- this is something I know I started doing after their name-switch in 2008. It just...sounds wrong....to call them the Rays.
The next thing to do is to try to pin down which
game Harry saw at the end of the story. Lessee. Zambrano started at Wrigley. In 2009. and it was late enough in the season (and the Cubs were doing well enough) that the management was looking into removing the curse (and 'Who do you like for the postseason' was not a silly question to ask....) So. Probably after the All Star Game. We have 7/27, 8/25, 8/30 and 9/15. I suspect that his start on 9/30 was too late in the season for the removal of the curse to really make a difference, as at that point, they were 8 games back and not going to the postseason. It was looking really, really unlikely on 9/15, too (5.5 games back in the wild card, 8.5 back in the division). Though I suppose the game Harry attended doesn't have to have been immediately following the case.