It doesn't exactly have to fill the entire basement, just the listening area. Although nothing is closed off so there is little to no room gain (If i've read correctly in other forums) I could take a picture of the area if you would like. Or try to explain it better haha.
Let me try to explain it more clearly. With normal speakers your distance from the listener assumption would be correct. Unfortunately subwoofers don't work that way unless you're almost right on top of them. In order to give you that feel it in your bones bass they need to move enough air to minutely alter the air pressure in the room. A little sub like the PL-200 will do a decent job in a
fully enclosed 1500-2000cuft (14x14x9) room but if you place one in the middle of let's say a 12,000cuft space the effect becomes something like that of a fart in a hurricane because it just can't move enough air. About the only things you can do are A) raise your budget, or B) get the most powerful sub that you can afford and put it as close as humanly possible to the seating location. Like maybe right behind the chair or sofa.
I've never heard that Dayton sub but I'll bet your father would be thrilled out of his mind having a sub his son put together for him or with him. Next year you could get him a second and set them up as end tables.