speaker redesign

Yes, it will place the drivers in a line source configuration, which may improve imaging, and horizontal dispersion, if everything else is done right.

If you are really looking to change the sound, I wouldn't be aftraid to look for a different crossover. You should get pretty drastic results with a new one.

You'll find AFTER measuring them at various points on the vertical axis whether or not they are more forgiving with the tweeter on top or the mid. All depends upon the drivers and the crossover. I'd suggest building the thing as a (sub)woofer cabinet on the bottom, and then a monitor on top, which will allow you to flip the top for voicing it optimally. Then you could make some in one cabinet, but you're actually better off acoustically (distortion, cabinet radiation spuriae, etc) by keeping them separate anyway! If you don't want to get this careful, then just stick the tweeter at ear level with the mid underneith, and keeping their distance as small as possible (usually...again, a function of MANY variables). You're just getting your driver's license here, so realize that this is a VERY complicated science/art, yet have fun with your first project.