[What was the M105?]
The M105 ran from 72nd & Broadway via West End Avenue and 11th Avenue to 42nd Street, then west to 12th Avenue. The northern half is covered by today's M57.
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[Was there really an M58?]
Yup. It was created in September 1989, to partially replace the former M103 on 59th Street. But first a little background...
The original route restructuring proposal sought to conslidate two redundant crosstown corridors, 57th Street (M28) and 59th Street (M103), into a single high-freqency corridor on 57th Street, AND accommodate large numbers of transfer movements from the M31 to both crosstowns. This would be accomplished by combining the M28, M31, and M103 into two overlapping L-shaped routes which would provide one-seat rides from the Upper East and Upper West Sides to the 57th Street corridor and frequent service along said corridor.
However, TWU-100 claimed that MaBSTOA work was being "given away" to TA, and went to arbitration. The first arbitrator ruled for TWU, so the Upper East Side component was implemented as the M58. Several arbtrations later, Transit won - the final arbitrator ruled that (1) Transit existed first and foremost to serve the riding public, not the unions, and (2) TWU had no business advocating AGAINST its TA members in order to support its OA members.
That ruling set the stage not only for the M31/M58 merger, but also for later TA-OA route swaps.