It is much more difficult to produce antiprotons than muons. Furthermore, my guess is that the proton-antiproton annihilation rate is much faster than the rate

It is much more difficult to produce antiprotons than muons. Furthermore, my guess is that the proton-antiproton annihilation rate is much faster than the rate of antiproton-catalyzed fusion. Muon catalysis doesn't have the annihilation channel (the heavy negatively-charged particle is always close to one H/D/T nucleus), so it will catalyze fusions all day until it decays. The antiproton can simply annihilate. That said, antiprotons probably would catalyze fusion at some rate. Whether it is higher or lower than muon catalysis, I'm not sure. If the antiproton orbital radius is too small, it may actually lower the capture cross-section for a neighboring hydrogen, even if the post-capture fusion cross-section is (almost certainly) higher.