So in an hydrogen atom, the total mass of the atom is equal to the masses of the proton, the electron, minus their net binding energy of around 13 eV. Making the total less massive than the sum of its parts by about 1 part in 100 million. As it also turns out, the electron follows the virial theorem, so that binding energy is actually in the form of -26 eV of electromagnetic potential energy and 13 eV of kinetic energy.
In a proton however, the total mass is equal to the masses of the three valence quarks plus the net binding energy, which is not only positive but accounts for 99% of the proton's mass. This is because the protons can never be in a free state, so while this binding energy is still positive, it is the minimum possible binding energy these quarks can have, and so attempting to dissassociate a quark increases the total mass of the system just like in the case for the hydrogen atom.
Now onto the question, what fraction of this total net binding energy can be considered as the potential energy of the gluon field between quarks and the gluons themselves, and what percentage can be considered to be in the kinetic energy of the quarks and gluons? The potential energy must still be negative (since it is still a potential well and the strong potential is attractive at nuclear distances), but the virial theorem no longer holds (because the strong potential doesn't follow an inverse square law), so the kinetic energy can no longer be simply negative half of the potential (and that would lead to a negative net binding energy anyway, but we know from above its positive). The kinetic energy must therefore be some multiple greater than 1 of the potential energy, and I am wondering if one has calculated what that multiple is. No doubt some lattice QCD and supercomputer shenanigans are needed to get the result, but surely it has been done?
TL;DR, the ~929 MeV of the proton, ignoring the ~9 MeV of the valence quarks, is some amount of negative potential and positive kinetic energy, say -200 MeV potential and 1129 MeV kinetic, for example. Those numbers are what I'm looking for.
(Note, I am aware that in actuality most of this energy will be taking the form of virtual quark-antiquark pairs, but these are in constant flux and so I am merely looking for the semi-classical baseline that these quantum fluctuations float around.)