It seems that most of the problems are gone.

By detailed study of StBTofCalibMaker class I figured out how the TOF path is calculated (a full length of arc starting at vertex and ending at TOF cell). Also, I started using calibration files for TOF (thank you, Daniel). I finally convinced myself that leadingEdgeTime is in nanoseconds.

All this enabled me to start identify particles in events where there are only two TOF-matched tracks.

File invBeta_vs_p.pdf shows \beta^{-1} vs. track momentum, where track with |nSigmaPion| closer to 0 (and <3) was used to calculate tStart (\beta and momentum of 2nd track are plotted).
File mSq_vs_nSigma.pdf shows squared mass vs. nSigmaPion for the events and tracks as above.
File deltat0.pdf  shows difference between tStart values calculated from two tracks if both them where recongnized as pions and not kaons and not protons, based on dEdx (double gaussian fitted).
File tStartTPC_vs_tStartRP.pdf shows average tStart from previous line (calculated from two pions) vs. time of collision as found in RP detectors.

Question: why there's no correlation visible between tStart from TOF tracks and time of collision calculated from timing in RPs?