We have studied the normal and superconductive state characteristics (resistivity, Hall coefficient, heat capacity and magnetization) of model strongly correlated electronic systems Lu x Zr 1-x B 12 with cooperative Jahn-Teller instability of the boron rigid cage and with dynamic charge stripes. It was found that these metals are s-wave dirty limit superconductors with a small mean free path of charge carriers l = 5 -140 Å and with a Cooper pair size changing nonmonotonously in the range 450 -4000 Å. The parent ZrB 12 and LuB 12 borides are type-I superconductors, and Zr to Lu substitution induces a type-I -type-II phase transition providing a variation of the Ginzburg-Landau-Maki parameter in the limits 0.65 1,2 6. We argue in favor of the two-band scenario of superconductivity in Lu x Zr 1-x B 12 with gap values Δ 1 ~ 14 K and Δ 2 ~ 6 -8 K, with pairing corresponding to strong coupling limit ( e-ph ~ 1) in the upper band, and to weak coupling ( e-ph ~ 0.1 -0.4) in the lower one. A pseudogap Δ ps-gap ~ 60 -110 K is observed in Lu x Zr 1-x B 12 above T c . We discuss also the possibility of anisotropic single-band superconductivity with stripe-induced both pair-breaking and anisotropy, and analyze the origin of unique enhanced surface superconductivity detected in these model compounds.