The mains hum signal on the recording, (50Hz Europe, 60Hz USA), could be used as reference when correcting the speed.
Use Audacity’s “Analyse”, “plot spectrum” to see where the mains hum fundamental frequency has been shifted to by the tape speed change.
[This sounds like a job for an autotune-type effect but with real-time adjustment of tempo, rather than pitch, to correct for the variations in tape speed].