Are there apps that enable "sticky" / "magnetic" / "docking" windows?
Divvy was my tool of choice for a while. It works like Zooom/2, so it will not fulfill your needs completely, just as the other suggestions on this question.

Stata 10 used to have 'magnetic' windows but the functionality disappeared, much to my sadness, in Stata 11. This change makes me believe that OS X must be resisting that functionality.

I think that the whole Exposé logic is working against that kind of functionality in the minds of many (but not mine: I am very sympathetic to your problem, I hate messy screens too).