Neutron-induced fission cross sections have been extracted for targets of ${}^{240,241,243}\mathrm{Pu},$ ${}^{234,236,237,239}\mathrm{U},$ and ${}^{231,233}\mathrm{Th}$ from ${E}_{n}=100\mathrm{keV}$ to $\ensuremath{\approx}2.5\mathrm{MeV}$ using surrogate $(t,pf)$ fission-probability data and a detailed statistical model to compensate for the difference between neutron-induced and $(t,p)$ reactions. This paper extends the results of previous work on the ${}^{235}\mathrm{U}(n,f)$ cross section, which serves as a proof-of-principle study. The $(n,f)$ cross sections are compared to earlier estimates based on the same surrogate data, but obtained using a more simplistic approach. The cross sections are also compared to accepted values where direct measurements exist and are consistently accurate to within 20% below ${E}_{n}\ensuremath{\approx}0.5\mathrm{MeV}$ and 10% at higher energies. The case of the ${}^{237}\mathrm{U}(n,f)$ cross section, simulated from surrogate $(t,pf)$ data, is investigated in greater detail to reconcile contradictory measurements in the literature.