The CS10 center channel unit appears to be the unit with the 5.25" woofers, so that's the one I suggest you get. I don't have any reason to believe that there is anything wrong with it. Do you? I see it as nothing more than the top 3 speakers and cabinet of your floor units lobbed off and laid on it's side. Should match up great.
Is it the 10" or 12" you can get for $120?
I don't suggest a 10" for a system of this "caliber." [some exceptions exist but at this budget, no] To be honest, if I were really serious about filling out the bottom end properly I'd be looking at a 15" or larger.
See... The way I see it, those TSI400s you chose, are in a middle ground that actually complicates things and screws up the budgeting for a balanced system. For many people, they would be fine without any sub at all. For others, who demand the bottom octave be reproduced, they won't quite cover it, and a sub is needed, however, adding a 10" sub to a room that already has these is not likely to add much of anything to bottom end extension. Yes it will allow you to play the bass above the bottom octave louder, or alternatively, take the bass load off of the mains so that they stay cleaner sounding. In the case of allowing the mains to play cleaner by crossing bass over to the sub, it doesn't make sense to have floor standing units full of woofers that aren't doing anything useful. So it goes back to my suggestion to run bookshelves all around if you are going to run sub/s (too late).
Keep in mind, that while the floor standing units are using smaller diameter woofers, they have very large boxes, which allows the boxes to be "tuned" to allow even small woofers to extend down pretty low while maintaining really respectable efficiency, especially if the driver dampening characteristics and Fs allow. Most sub-woofers these days, are trying to be more compact than they really should. They are very small little cubes with a driver that barely fits one face of the cube. The result is a very inefficient power hungry device that, in many cases, is not likely to play much "lower" than the floor standing front mains they may be getting paired up with. To get powerful performance in the 20-35hz range, you can either attack the problem with powerful amplification and "small boxes" combined with long throw small drivers, or relatively mild amplification and "big boxes" with relatively ordinary "throw" large woofers (both options are expensive, but even more expensive, is combing the big box, with the big amp, and the big long throw driver, which will basically assassinate your internal organs). In the budget range, you tend to get small boxes and small amplifiers and relatively short-throw woofers all in one, which means that you're still pretty much stuck with ~30hz as your realistic bottom end. Technically speaking this is plenty "low" for 99.9% of what you will ever possibly hear or not hear through your system.