The speed of the action is dependent solely on the lip width. The narrower the lip the faster the wiggle.
For a tight action rather than a wide action, the coffin is a good choice. I tested various lip shapes in a direct comparison and the coffin was narrower than the others.
Depth is just about finding the sweet spot for the tow eye location. Too far forward or back and you lose depth. No one can tell you where this is, you have to find it by testing. Examine pictures of similar baits and start there.
A heavier wood will give a tighter action than balsa. But all you need to do is spread the ballast out on a balsa lure to achieve a tighter/narrower action. It would make more sense to use a heavier density wood.
Dave