Seems awesome to me!
A question and two criticisms:
Q: When you say that deadly marksmanship "stacks" with Imp Crit, do you mean that it's doubled with the rest, or that it's added after the doubling?
C: The between the eyes ability is kinda overpowered if you fifth level. I mean, even with the DC probably being around 15 or 16, you're gonna have monsters having to roll 10+ more often than usual with the deadly precision ability, especially when they finally get Imp crit at 9th level (or 8th, if they multiclass fighter for the quicker benefit). Also, maybe elves should be able to count it as favored class. Ideas for that would be to have them choose at first level, or to have the first one they take a level in be the FC (probably the second).
Anyway, I've tried countless times to make archer classes, none of which even made it past the drawing board.
BTW, if you don't copyright this, I'll probably start selling it.