If you're looking for a dependable subwoofer that will produce smooth, deep bass, look at doing an 8" woofer in a ported enclosure. You can fit an 8" ported box in the space you have and you'll have a lot better and more pronounced bass with that than you will with the Pioneer 10 in a sealed box. The Sundown E8 is a 200 watt RMS woofer that will take twice it's RMS power all day every day and the Pioneer will not take 1100 watts on a good day.... at least not for more than about 45 seconds, I would suspect.
The PPI would be a good amp for your highs and if you're not going to amplify the rear speakers, you could by the dual two ohm E8 and run it on two channels of the PPI at 225 wpc, which would be a perfect match for that sub as far as over powering it safely.
And if not the Sundown sub, something other than a Pioneer sub would be my suggestion. I like their head units but I've never had good luck with Pioneer speakers sounding very good or holding up well, especially subs. But that's just my experience, so take it for what it's worth.