If you have Improved Precise Shot, Sharp Shooting is useless, as SS halves cover bonuses, IPS negates.
I think that Imp Rapid Shot has Manyshot as a prereq.
IIRC, anyways.
Manyshot, Greater Manyshot are good, especially if you multi into scout.
Shot on the Run may or may not be useful.
You may want to check out the Crystal Keep Feat Index for the archery feats, there's some very good feat options there. Though, whether or not it'll be allowed is, well, questionable.
Order of the Bow Initiate. Unleash the awesomeness[some may read it as cheapness]!
With Greater Manyshot (though, Ranged Precision might not work with it).
And start shooting everything that moves. And after the second level, you can do so when threatened without a care in the world.
From Complete Warrior, page 68. You'll need 5 ranks in Craft (bowmaking) and 2 in Know (religion), though.
Your DM does not sound like fun.
What kind of bow? Long or Short?