Alpine Subwoofer + Fostex Full range?

Hello! I'm building my main speakers with fostex FF165WK + Fostex FT17H speakers. The speakers will be floorstanding, so I have some empty volume left in each speaker.

I was planning to add a subwoofer for the system. I live in Argentina, so good subwoofers are very expensive and difficult to find. So I was thinking what I have here at reasonable price. I found this car subwoofer, 8" Alpine S-W8D4, with a recommended sealed box of 0.30 ft3 / 8.5 liters and that's almost the exact room left that I have for an aditional driver.

Fs 48hz
qts 0.54
xmax 13mm
xmech 40mm

I will be using bi-amp of course.

What do you think? Using alpine with fostex is some kind of herecy?