You can adjust tracks precisely in time by using something like Voxengo's free Sound Delay plugin. You may enter amounts by distance or by milliseconds - or larger values.
If you want a single track moved forward, you may have to delay the others.
Remember, any spill on the mic's will be delayed as well.
Alternatively, and something that I have not tried, is to use Generate Silence and specify milliseconds (for example, 1 and 1/2 millisecond is 0.0015 second) or numerically enter such an amount for deletion at the beginning of the track. Again, I have not tried this method with AP, so I don't know whether such values can be specified.
The plugin is quite straight forward.
quantizin notes
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