Hmm, I do agree that your priorities are correct. I think COOH gets a higher priority than C3 because COOH has 3 bonds to O, whereas C3 has 1 bond to Cl, 1 bond to H, and 1 bond to C.
When you have the lowest priority as a wedge in a Fischer diagram, I don't think you can simply switch between R and S. I think you have to swap the lowest priority molecule with a dashed molecule, and then determine the configuration. I'll attached a picture since my explanation may be confusing.