not a bad look'n room there.
your budget is reasonable.
four sealed subs. 4 cubic feet each.
Dayton Audio RSS390HF-4 15" Reference HF Subwoofer 4 Ohm
Dayton Audio DVC385-88 15" DVC Series Subwoofer
Behringer NU3000DSP iNUKE 3000 Watt Power Amplifier with DSP
without any room gain, that will give you around 115db+ at 20hz.
with your room, i'd guess that you will have full reference into the low teens.
the -hf driver has low inductance and the design choice was to use a little larger enclosure for a little better sound quality.
you could cross them up to several hundred hz if you need to, as there is no way your mains are going to keep up with this bass system.
drivers would be wired in parallel and run two per channel.
behringer specs peak power, so in reality, you'd have about 500 watts per driver.
the dsp is easy to use and has all kinds of features should you need them.
if you buy from parts express, it is in stock, it ships free, and if you have a problem, they have a good reputation for taking care of their customers.
how you make them look is up to you.
edit: not sure if shipping is free to alaska from p.e.