My Boston tweeters are mounted in the windesheild frame aimed at the windshield. The glass gives it extra "boost" and the top down issue is no more!! I use the door speakers strictly for mid's.

 

I agree with Lucid. Rear speakers helped create full sound. Also component speakers did wonders. Try to mount your tweater higher on the door.
By the way, this head unit has the ability to set time delays for each of the speakers. This helped with the sound stage distortion!
Power to the front speakers also helped. I have a 4 channel amp, 2 channels pushing the components in the doors (JL pro's), and 2 channels running the sub. I used the head unit to push the rear's (4 Alpines). Sound is terriffic, and no problem hearing lyrics at 90 mph!