We report observed and derived timing parameters for three millisecond pulsars (MSPs) from observations collected with the Parkes 64-m telescope, Murriyang. The pulsars were found during re-processing of archival survey data by Mickaliger et al. One of the new pulsars (PSR J1546-5925) has a spin period $P=7.8$ ms and is isolated. The other two (PSR J0921-5202 with $P=9.7$ ms and PSR J1146-6610 with $P=3.7$ ms) are in binary systems around low-mass ($>0.2 M_{odot}$) companions. Their respective orbital periods are $38$.2 d and $62.8$ d. While PSR J0921-5202 has a low orbital eccentricity $e=1.3 times 10^{-5}$, in keeping with many other Galactic MSPs, PSR J1146-6610 has a significantly larger eccentricity, $e = 7.4 times 10^{-3}$. This makes it a likely member of a group of eccentric MSP-He white dwarf binary systems in the Galactic disk whose formation is poorly understood. Two of the pulsars are co-located with previously unidentified point sources discovered with the Fermi satellites Large Area Telescope, but no $gamma$-ray pulsations have been detected, likely due to their low spin-down powers. We also show that, particularly in terms of orbital diversity, the current sample of MSPs is far from complete and is subject to a number of selection biases.