A quick review of your drawing indicates to me that your area would be considered an "Extreme Room" size (over 5,000 cu. ft.). It takes a big, powerful and expensive subwoofer to fill such a volume, and usually multiples. Can you do with less? Sure, especially for music. Not everyone, including myself, listen at reference levels (over 100 dB at the listening position).
I think your selections are very good ones, but you'll need as much as you can afford in that cavernous volume. I'd also consider adding a second sub down the road when funds become available, if the sub isn't filling that volume to your satisfaction or you are having problems with uneven frequency response at the listening position.