Layered ternary (MnX₂Te₄)(X₂Te₃)_n (X = Bi or Sb, n = 0-3) tellurides are intensely studied as perspective magnetic topological insulators: MnBi₂Te₄ and MnBi₄Te₇ demonstrate the quantum anomalous Hall effect up to several Kelvin. To enlarge the temperature range for this quantum behavior, the materials require a net magnetization and a high Curie temperature, T_C. Recently, we found that Mn enrichment and Mn/Sb site intermixing increase the T_C from 30 K in MnSb₂Te₄ to 58 K in Mn_2.01(1)Sb_1.19(1)Te₄. Here, we synthesize the utmost manganese-rich members of this materials family, with an average Mn content of 28-32 at. % and the record T_C = 65-73 K nearing the liquid-nitrogen threshold. By combining single-crystal X-ray diffraction, ab initio modeling and bulk DC magnetization, we pinpoint the relationship between the lattice symmetry and the magnetic order. The trigonal Mn_1.90(1)Sb_1.39(1)Te₄ phase with manganese atoms in the van der Waals gap hosts the highest-T_C ferrimagnetic state. We get the first insights into its electronic structure and topological nature by ab initio modeling using density functional theory. Initiated by the filling of the van der Waals gap, the compound mimics a structural transition from a trigonal (sp. gr. R3̅m) to a cubic lattice (sp. gr. Fm3̅m), which is reminiscent of the structural polymorphism of the Ge-Sb-Te thermoelectrics.