The effect of doping with Ti, Ta, SiC in complex with synthesis temperature on the amount and distribution of structural inhomogeneities in MgB₂ matrix of high-pressure-synthesized-materials (2 GPa) which can influence pinning: higher borides (MgB₁₂) and oxygen-enriched Mg-B-O inclusions, was established and a mechanism of doping effect on j_c increase different from the generally accepted was proposed. Near theoretically dense SiC-doped material exhibited j_c= 10⁶ A/cm² in 1T field and H_irr =8.5 T at 20 K. The highest jc in fields above 9, 6, and 4 T at 10, 20, and 25 K, respectively, was demonstrated by materials synthesized at 2 GPa, 600 °C from Mg and B without additions (at 20 K j_c= 10² A/cm² in 10 T field). Materials synthesized from Mg and B taken up to 1:20 ratio were superconductive. The highest j_c (6×10⁴ A/cm² at 20 K in zero field, H_irr= 5 T) and the amount of SC phase (95.3% of shielding fraction), T_c being 37 K were demonstrated by materials having near MgB₁₂ composition of the matrix. The materials with MgB₁₂ matrix had a doubled microhardness of that with MgB₂ matrix (25±1.1 GPa and 13.08±1.07 GPa, at a load of 4.9 N, respectively).