I don't know if that PSU design is proprietary, but it is certainly non-standard and would be difficult and expensive to replace, especially on a computer that's what, 2 years old now? I don't think that it would be worth the investment. At least you have the 400W model and aren't stuck with a 300W.
I think that you would be better off getting a card that will work with your current PSU. The GTS 250 may indeed be a better choice for you. It would still be a monster improvement over what you have. As long as your PSU has one 6-pin PCIe plug, which I think it does, you should be OK. One of the improvements of the GTS 250 compared to the 9800GTX+ is reduced power consumption; it only requires 1 6-pin plug instead of 2. Astro is the Shuttle guy here, and would know way more about anything regarding Shuttles than I do.
PSU aside, we'll need to know if the card will fit in that itty-bitty case. IIRC, Astro has managed to fit first a 7950GX2 and later on an 8800GTS 640MB into his Shuttle case, so I'm sure that it's possible, but once again he's the guy to ask.
In the meantime, I'll keep my eyes open for a bargain GTS 250 for you.
"They should rename the team to the Washington Government Sucks. Put Obama on the helmet. Line the entire walls of the stadium with the actual text of the ACA.
Fix their home team score on the board to the debt clock, they can win every game 17,000,000,000,000 to 24. Losing team gets taxed by the IRS 100%, then droned."