Cross sections for the reactions $e^+ e^-to K^0_S K^0_Lpi^0$, $K^0_S K^0_Leta$, and $K^0_S K^0_Lpi^0pi^0$ from events with initial-state radiation

We study the processes $e^+ e^-to K^0_S K^0_Lpi^0gamma$, $K^0_S K^0_Letagamma$, and $K^0_S K^0_Lpi^0pi^0gamma$, where the photon is radiated from the initial state, providing cross section measurements for the hadronic final states over a continuum of center-of-mass energies. The results are based on 469~$fb^{-1}$ of data collected at or near the $Upsilon(4S)$~ resonance with the BaBar detector at SLAC. We present the first measurements of the $e^+ e^-to K^0_S K^0_Lpi^0$, $K^0_S K^0_Leta$, and $K^0_S K^0_Lpi^0pi^0$ cross sections up to a center-of-mass energy of 4~GeV, and study their intermediate resonance structures. We observe $J/psi$ decays to all of these final states for the first time, present measurements of their $J/psi$ branching fractions, and search for $psi(2S)$ decays.