A method is proposed to determine the M1 nuclear transition amplitude and hence the lifetime of the "nuclear clock transition" between the low-lying (~8 eV) first isomeric state and the ground state of ²²⁹Th from a measurement of the ground-state g factor of few-electron ²²⁹Th ions. As a tool, the effect of nuclear hyperfine mixing in highly charged ²²⁹Th ions such as ²²⁹Th⁸⁹⁺ or ²²⁹Th⁸⁷⁺ is used. The ground-state-only g-factor measurement would also provide first experimental evidence of nuclear hyperfine mixing in atomic ions. Combining the measurements for H-, Li-, and B-like ²²⁹Th ions has a potential to improve the initial result for a single charge state and to determine the nuclear magnetic moment to a higher accuracy than that of the currently accepted value. The calculations include relativistic, interelectronic-interaction, QED, and nuclear effects.