IMHO, no tape deck regardless of how expensive cannot match transparent processing in digital domain.

The most transparent process is by doing the shift in two phases - playback rate change and then resampling.
Playback rate change is always lossless, and resampling using SoX or iZotope's MBIT is as transparent as it gets.

All other disturbances are present in the recording and the process only made them audible because those shift from inaudible spectrum to audible.