Can you get it to click into the index for the large ring with the cable slack?

Help me help you buddy.

EDIT: and the limit screw could be the problem- just because you can shift the chain there, doesn't mean the shifter can get the chain there its pawl into the index for that gear. Now that you've tightened the cable, you might be able to swing the FD up, but the shifter needs a little over run to get the pawl to engage. You know how you need to pull a pretty good amount of cable before the shifter clicks? Well, with a tighter cable and a limit screw, you could be moving the FD all the way to the limit screw before you get to the click- thus, you're operating within that pretty good amount of cable pull and not letting the shifter get a full swing.