Obtaining an IR from a sine sweep without the dry sweep
If this is used for channel sounding then you aren't concerned with the actual accuracy of your turntable (causing a frequency shift) in which case I suggest measuring the response in a static condition (non-changing channel) and determining the least square linear fit of the frequency sweep (I would assume but don't know that the test pattern would be a linear sweep) and then from that reconstruct a reference sweep to then use for channel estimation.
Measuring the frequency involves using some for of frequency discriminator process, most of which are also sensitive to amplitude variation, so I recommend hard-limiting the signal prior to the discriminator. Also pay attention to the relationship between instantaneous frequency and the underlying frequency of your ramp as detailed in this &quot;DSP Quiz&quot; question:  Simulation of a Frequency ramp