The output settling time can be decreased by decreasing the time constant of the lock-in- amplifier (LIA). A practical solution is to reduce time constant of LIA as the reference frequency (chopper frequency) is increased.

Actually higher time constant gives better S/N ratio. But for high TC measurement slows down. In you case it is 10 second. So now you can decide the reasonable TC.

It is assumed that your detector signal will be in form of a DC voltage if your radiation is kept unchanged. This signal is contaminated by the noise of the detector.

So, If the noise is correlated one can eliminate the noise by subtracting the off signal from the adjacent on signal. To achieve correlation one may make the off time short and the on time of an equal interval.

I would like to propose that you reduce the chopper time and see how instruments reach to steady sate.

On the other side too short time may not allow the detector and the electronics to reach their steady sate conditions.

If you van acquire the waveform pf your signal, then you can analyze it by FTT to determine it frequency content.

The DC value must be the targeted detector reading.

If the steady sate value is drifting It may be due to the slowly time variation in the signal.

Best wishes