A quick search on newegg popped up an ATI X300, but it uses the new "Hypermemory" thing, which is (I believe), ATI's answer to the Nvidia Turbo Cache card. Stay far far away from these. Not that the X300 is a hot performer anyway, but this just makes it worse.
And yes, low profile is simply a space consideration due to the limited size of the box. It has nothing to do with performance restrictions. What you suggested is exactly what I'd do. Either cut up the case, or just take the side off completely and live with it. Low profile cards are usually hard to find, and give up something in performance somewhere to the full size ones. Even if it's just a fan.