Do I need a subwoofer? Which brand and model?

One interesting test I tried was to shut the main speakers off. This allowed me to independently test the effect of the subwoofers and adjust settings until I got what I liked the most. This was an useful test for me,

This is the problem with having no experience, along with the commitment to not get any because you think you're a scientist. All you do is list other people's opinions on stuff and select only the factual info that you think is important, while not addressing other issues because you simply don't know how to deal with them. The only science that applies in your case is psychology.

"But, in general the higher the low pass filter setting the easier it becomes to localize the sub."

"I've read many people say that the sub should not call attention to itself and you only realize it was in the system after you turn it off and miss its effects."

Pick one. In the first paragraph, you're telling him set the sub up so it can be localized. In the 3rd paragraph you're telling him to set it up so it can't be localized.

"Measuring will help you set it. My understanding is to set the phase control such that it maximizes the bass response. Doing so will let you turn the overall level down and give you some headroom; you are effectively taking advantage of the room by not destructively interfering with the main speakers."

Maybe you should actually try it. The logic in that paragraph has more holes in it than a French Poodle that was hit with a 12 gauge shot gun. Give him some headroom? That implies that he has none to begin with. How do you know that?

"you are effectively taking advantage of the room by not destructively interfering with the main speakers."

That doesn't even make sense. You take advantage of the room by not destructively interfering with the main speakers? Scientist, my ass.