Originally Posted by Rolla

I have no idea if that Ritchey headset will work, but I suspect it will. And that's the right tool for removing headset cups (although they do come in different sizes).

But what might be causing your "wobble" is that the stem isn't being pulled onto the headset stack sufficiently. Unscrew and remove the top cap and ensure that there's a 2mm gap between the top of the steering tube and the top of the stem. If there isn't, remove the stem, add a thin spacer under (or above) it, then retighten the top cap and the bolts.