You are not forced to use SMD capacitors :-), given the hard job you're facing, I would consider using ordinary caps. The motherboard won't be pretty anymore but it'll be an easy task compared to this.
About twisting caps, indeed there's a risk to damage pads but usually only when the leakage and the corrosion are really big. And then you have very few alternatives, the pads are not thermal conductive anymore and are really hard to desolder.
