If the Founders could do this, completely change their physiology and change it back with relative ease, why have shape-shifting spies when they could undergo this process, thus avoiding the whole blood test pitfall? The spies wouldn't personally like it, but they'd make the sacrifice for the greater good of the Dominion or such, right?

I don't think this is such a gaping inconsistency, actually. The Founders' ideology is presented repeatedly as "changelings rule, solids drool," to grossly oversimplify, and I don't really think we have to look any further than that for explanations why not.