Determining SINAD from measured data
Similar to the determination of the confidence intervals when estimating the population variance from a smaller sample, with a limited amount of data you will have a large variability in your estimates. There really is no way around reducing this error or variability other than taking more data (to the extent it is stationary).
For an optimized approach to measuring the SINAD, I suggest using correlation of your distorted signal with the reference waveform before any noise is added. I detail this approach further at these post:
How can I find SNR, PEAQ, and ODG values by comparing two audios?
Noise detection