Nearly free electron (NFE) states with density maxima in nonnuclear (NN) voids may have remarkable electron transport properties ranging from suppressed electron-phonon interaction to Wigner crystallization. Such NFE states, however, usually exist near the vacuum level, which makes them unsuitable for transport. Through first principles calculations on nanocomposites consisting of carbon nanotube (CNT) arrays sandwiched between boron nitride (BN) sheets, we describe a stratagem for stabilizing the NN-NFE states to below the Fermi level. By doping the CNTs with negative charge, we establish Coulomb barriers at CNTs walls that, together with the insulating BN sheets, define the transverse potentials of one-dimensional (1D) transport channels, which support the NN-NFE states.