In addition to the radioactive problem, you are correct about the energy balance, too. As energetic as the DPF is, you would still be fighting an uphill battle against the binding energy curve. And thorium is way beyond iron on the curve, where fusion starts to absorb energy rather than release it. You would need even more energy than the DPF can provide.
Violent supernovae, anyone? We could cook-up some gold and silver while we’re at it.
About the only other way a DPF might “burn” thorium (a very unlikely longshot) is if some of the energetic protons caused a secondary release of neutrons by way of the spallation effect or something similar to it. In fact, shooting a beam of energetic protons at a lead target to generate a secondary shower of neutrons is one of the ways physicists have proposed for a thorium reactor. But such an effect or something similar might not even work in a plasma.