Substituted lithium transition-metal (TM) phosphate LiFexMn1-xPO4, materials with olivine-type structures are among the most promising next generation lithium ion battery cathodes. However, a complete atomic-level description of the structure of such phases is not yet available. Here, a combined experimental and theoretical approach to the detailed assignment of the P-31 NMR spectra of the LiFexMn1-xPO4 (x = 0, 0.25, 0.5, 0.75, 1) pure and mixed TM phosphates is developed and applied. Key to the present work is the development of a new NMR experiment enabling the characterization of complex paramagnetic materials via the complete separation of the individual isotropic chemical shifts, along with solid-state hybrid DFT calculations providing the separate hyperfine contributions of all distinct Mn-O-P and Fe-O-P bond pathways. The NMR experiment, referred to as aMAT, makes use of short high-powered adiabatic pulses (SHAPs), which can achieve 100% inversion over a range of isotropic shifts on the order of 1 MHz and with anisotropies greater than 100 kHz. In addition to complete spectral assignments of the mixed phases, the present study provides a detailed insight into the differences in electronic structure driving the variations in hyperfine parameters across the range of materials. A simple model delimiting the effects of distortions due to Mn/Fe substitution is also proposed and applied. The combined approach has clear future applications to TM-bearing battery cathode phases in particular and for the understanding of complex paramagnetic phases in general.