[en] We report our extensive ⁵⁷Fe-, ⁷⁵As-, ¹³⁹La-, and ¹H-NMR studies of La_0.8Y_0.2FeAsO_1-y (La_0.8-Y_0.21111) and LaFeAsO_1-yH_x (La1111H), where doping yttrium (Y) and hydrogen (H) into optimally doped LaFeAsO_1-y [La1111(OPT)] increases T_c=28 to 34 and 32 K, respectively. In the superconducting (SC) state, the measurements of nuclear-spin lattice-relaxation rate 1/T₁ have revealed in terms of a multiple fully gapped s_±-wave model that the SC gap and T_c in La_0.8Y_0.21111 become larger than those in La1111(OPT) without any change in doping level. In La1111H, the SC gap and T_c also increase slightly even though a decrease in carrier density and some disorders are significantly introduced. As a consequence, we suggest that the optimization of both the structural parameters and the carrier doping level to fill up the bands is crucial for increasing T_c among these La1111-based compounds through the optimization of the Fermi surface topology. (author)