Running without the servo cover should be fine, Scott. Its not really much of a brace, but rather a hold-the-servo-in/mount-the-battery-strap/mount-the-transponder piece.
For the others, those little vertical braces are still there in the pics. Look closer; if they weren't there you'd see dremel-marks from the process of removing them.
And you'd be surprised what those little braces do for the chassis stiffness. The outside walls look stiff (and nice and tall) but they like to bow outwards because they're straight along there. I really don't recommend removing the little braces. Also, those little braces make excellent little areas to put lead weights when your car is too light because of the lipo.
Also, Lipo + speed control in center = ace