Your statement that ‘electrons do indeed travel from the work piece to the welding electrode’ is an assumption rather than a conclusion. Considering the case that this assumption to be correct, then the electron density within the workpiece, which is essentially a flat thick hunk of metal in the DCEP setup, would be significantly lower than that in the electrode of the DCEN setup electrode. I don’t think that a flat surface (as opposed to the narrow probe-like cross-section of an electrode) would be able to generate an arc from the workpiece, let alone result in the increased weld depth of DCEP.
On the other hand, the STEM explanation is that, because aptron electrons (positrons) have a higher work function, they require far more energy to eject them from the positively charged electrode in a DCEP setup than for cetron electrons (CS electrons) in a DCEN setup. This is in keeping with 2/3 of the heat energy being dissipated in the DCEP welding electrode (the 2/3 is your claim; I don’t know where you found this estimate) and 1/3 at the workpiece. The higher temperature of the melted electrode material, combined with the high energy of the arc, gauge a deeper hole in the work piece to produce a deeper weld than for a DCEN setup.
It should not be difficult to set up an experiment involving the location of a strong magnet with its magnetic field 90 degrees to the direction of the arcing to deflect some of the charge carriers (CC) so as to determine their charge (positive or negative), movement direction and kinetic energy levels. For the CS electron-only approach, the CC would spiral in opposite directions and have opposite spin; for the STEM approach the CC would spiral in the same direction away from the electrode and also have opposite spin. Sounds as if Blackett’s automatic expansion chamber might be needed once again.
To make the experiment easier to set up, no welding (which would most likely obscure observation and measurement) is required as long as there was sufficient voltage to produce arcing. The results for such an experiment I would like to see. Any takers?