Actually the partons , as the constituents of the proton (and other hadrons) are called ,have been studied experimentally through the years by scattering experiments , and their distribution functions published, from various experiments.
At low energies of experiments this pictorial representation of the proton is valid, with only the low mass quarks and anti quarks.
As the energy of the experiments goes up, higher masses can be seen in the extraction of information from the experiments.
The latest experiment I find is with the Atlas experiment at LHC.
It is complicated mathematically, so the popularized versions have to be seen with caution of their being close to non-sense.
You say:
I know that the quarks exchange color... but do they truly change types?
As long as conservation laws are obeyed, yes , through virtual interactions with other quarks.
I know that in macro-space you have virtual particles popping into existence and then being annihilated.
This is another popular miss conception, by trying to popularize the mathematical theory of quantum field theory. This popping can happen only where other interactions exist, not in completely empty space.
But is there space inside the proton for this to happen?
Yes, the proton is not an elementary zero point particle, the way the constituent quarks etc are. It has a spatial volume and complicated chromodynamic interactions are the rule.
