A special method has been applied to synthesize HTSC samples of Bi1.7Pb0.3Sr2Ca(n-1)CunOy with increased local inhomogeneities, using solar energy for the melting and following superfast quenching of the melt (SFAQ-T technology). This study carried out a comparative analysis using low-frequency torsional vibration and resonant vibrating reed spectroscopy methods. The results showed a possibility for the existence of high-temperature superconducting precursors with Tc = 107-138 K and the potential advantages of the application of the resonant vibrating reed method.