Read through this. It might help.
http://www.mrgearhead.com/faq/basssetup.html
How are the strings wound on your tuners? From the bottom up, or the top-down? Best to wind them from the top down as this keeps more tension on the nut, which is consistent with what you are describing when you press down on the string at the nut.
Neck-thru and bolt-on setups are very similar, except that you have the option of using a shim or tilt screw adjustment to change the neck angle a bit. This can be helpful if you have a very high action at the upper frets while having a decent action at the lower frets.
Truss rod adjustment is much the same. The Gary Willis info at the top of this forum works really good.
Remember: The truss rod isn't for setting string height. It is for adjusting neck "relief" (the small amount of forward bow all necks need). String saddles are for adjusting string height.
If your E is sounding dull and dead, you probably need to adjust your pickup height up a bit near that string. This will help bring it out a bit better. But do the neck setup and adjustments first.
Mag...