In the end it all boils down to the fact that visible light an laser operate on the energy scale of electronic transitions whereas nuclear transmutations occur at the vastly different energy scale of the strong force. This huge separation between electromagnetic interactions and strong nuclear interactions is btw also the reason why radioactive material is not typically green glowing goo.
You previous calculations are for creating light pressure sufficient for fusion, that's a uniquely energy consuming process, You can't reuse those numbers here because they are not trying to crush Uranium atoms together.
But likewise I could not find concrete details for the proposal.
The limit comes from the following process: Thanks to quantum mechanics there is an uncertainty principle between position and momentum. Less known it the uncertainty between time and energy. (If you have studied classical mechanic you will recognize that the variable pairs are the same that you know from Noethers theorem [3].)This implies that nature can (and will) violate conservation of energy by an amount deltaE for a time deltat up to hbar/deltaE. One such process is the creation of a electron-positron pair out of vacuum. That violates energy conservation by about 1 MeV and you have to return the (virtual) particles within hbar/1MeV or approximately 6e-22 seconds. If however the electric field is sufficiently large that the particles get accelerated to an energy of 1 MeV within that time they get to stay. An electric field that can do that has a field strength of 1.3e18 V/m.
At that intensity the laser light does not simply propagate through vaccuum as predicted by Maxwells equations, but is producing a pair plasma and gets damped. The process is fairly well described by QED. We are currently trying to get laser up to that intensity and to make accurate measurements of this QED effect as it does not only work for electron-positron pairs, but arbitrary particle-antiparticle pairs. Experimental deviations from the QED predictions would therefore imply the existence of additional light particles (and antiparticle) that we have not found through other methods.
1: https://en.wikipedia.org/wiki/Schwinger_limit