There may be two issues in play here. First, it appears the Ritchey headset may have a shorter stack than the original headset, so the top nut bottoms out on the steer tube before locking against the lower pieces. This is easily remedied with a a spacer(s).

Second, if the headset can't be adjusted without either play or binding, this suggests that the upper and lower races are not properly aligned. This can happen if the pressed-on pieces (crown race, and upper and lower head tube pieces) are not fully seated or if the crown race seat and/or head tube faces are not properly milled.

Look for gaps between the crown race and fork crown, and between the head tube pieces and frame. If you see a gap, that part is not fully seated. Use a crown race seater tool (aka "slide hammer") and/or headset press to fully seat the parts. If you're lucky, that should fix the problem. If the problem persists, take the frame and fork to a well-equipped shop to be milled into alignment.