Perhaps this is incorrect, but this is what it appears with regards to the "dual lows" at the surface.
The wave which comes inland looks like the main wave which develops along the cold front. The secondary low looks to be the one which forms from the modeled SE convection. This low then completely blows up due to 1) phasing with the vigorous s/w energy with the trough and looks like enhancement from the jet max surrounding the base of the upper trough. This outcome then completely covers the solution with puke.
It looks like the LLJ with the frontal wave is nothing out of the ordinary...but with what happens b/c of that other low and the significant strengthening which occurs you get a response in the LLJ to go wild...forgetting even the wind potential this then increase theta-e advection, moisture transport, and PWAT values into the region...add extra lift and extra moisture and the response is bonkers QPF.
Naturally, as a low develops and strengthens along the front, you'll get a LLJ increase, however, the big question here is what is the driving point behind the strengthening of the frontal wave? Going to rule out dynamics here based on the structure of the ULJ and MLJ...so the next explanation would be a tightening thermal gradient...but is it possible this is being enhanced b/c of that secondary low?