Two SMPS simulations are essentially the same but one malfunctions...why?

Here are two like-for-like LTspice simulations…one works well but the other doesn’t. Why is this?
Each simulation has two offline buck converter LED drivers.
In one simulation there is one mains source supplying both bucks. But in the other simulation each buck has its own mains source. That is the only difference between the two simulations.
So why does the one with a single mains source show a disturbance in its inductor current i(L3) from the 2ms point onwards? The other simulation doesn’t malfunction like this. Why? They are both essentially the same.

LTspice sims and pdf schematics attached

Strange indeed. I suspected the AC source impedance, or the maximum timestep setting, might account for the difference; but playing with those didn't resolve the issue.

Would both circuits really be connected to a single AC source that way?
Or would there be separate AC windings feeding each circuit?