Strontium doping transforms manganites of type La_1-xSr_xMnO₃ from an insulating antiferromagnet (x = 0) to a metallic ferromagnet (x > 0.16) due to the induced charge carriers (holes). Neutron scattering experiments were employed to investigate the effect of Sr doping on a tailor-made compound of composition La_0.7Sr_0.3Mn_0.1Ti_0.3Ga_0.6O₃. By the simultaneous doping with Sr²⁺ and Ti⁴⁺ ions, the compound remains in the insulating state so that the magnetic interactions for large Sr doping can be studied in the absence of charge carriers. At T_C = 215K, there is a first-order reconstructive phase transition from the trigonal R-3c structure to the orthorhombic Pnma structure via an intermediate virtual configuration described by the common monoclinic subgroup P2₁/c. The magnetic excitations associated with Mn³⁺ dimers give evidence for two different nearest-neighbor ferromagnetic exchange interactions, in contrast to the undoped compound LaMn_yA_1-yO₃ where both ferromagnetic and antiferromagnetic interactions are present. The doping-induced changes of the exchange coupling originates from different Mn-O-Mn bond angles determined by neutron diffraction. The large fourth-nearest-neighbor interaction found for metallic manganites is absent in the insulating state. We argue that the Ruderman-Kittel-Kasuya-Yosida interaction reasonably accounts for all the exchange couplings derived from the spin-wave dispersion in metallic manganites.