the best theory so far is that of Widom-Larsen

Widom-Larsen requires an implausible mix of scales. The effective mass of heavy electrons in the solid state is a collective phenomenon happening over distances and time-scales that are large relative to the nucleus and nuclear time-scales and affect the dynamics of the electron's interaction *with the lattice, on those scales*. To impute to these large-scale effects efficacy at the nuclear scale is very unlikely to be correct.

Consider a car analogy: a car moving along a freeway in dense traffic interacts with all the cars around it. If the driver accelerates, they will pull up close to the care behind and that driver may speed up a bit too, sending a diminishing wave of acceleration through the traffic, so compared to the same car alone on the road the car in dense traffic appears to have a much higher effective mass. Alone, you hit the gas and speed up a lot. In traffic, you hit the gas and speed up a little bit. That's what the electron in the surface looks like: a car in traffic.

But on the scale of car-car interactions, the "bare" mass of the car is what matters. If two cars collide you get an energy of 0.5*m*v^2, not 0.5*Meff*v^2.

Yeah, there are multi-car pileups that muddy the analogy, but they add up to nothing like the effective mass of the whole traffic block, so there. And the difference in scales between "cars and traffic" is tiny compared to the difference in scales between "nuclei and the lattice", so the effect that analogy hopefully makes obvious will be that much larger in the latter case.