For a noise test, one can measure with a short, thus essentially without the noise from the references. One way to look at it would be the Alan variance curve.
Using just one 0 measurement (thus manual "auto" zero) is a two sided way. It increase the noise of the zero measurement (as only a single 10 PLC conversion is used) but would reduce the noise from the readings of the input. In addition it will also hamper the suppression of 1/f noise due to the AZ readings. So it depends on the signal to measure if this is a good idea. It can help if the measured voltage is very noisy, but it would increase the noise if the measured source is low noise. To a certain degree, spending less time for the zero measurement could be a good idea, but it depends on the signal and a 10:1 ratio would be something for rather noisy signals and it shift the 1/f suppression to around 110 PLC, compared to 20 PLC for for conventional 10 PLC radings.
I have a suspicion the Keithley meters like DMM7510 are doing it a little like this: using less time on zero measurement and use some averaging on the zero reading instead. At least this could explain there relatively poor noise performance in the 10-100 mHz region, when using the internal AZ mode with a low noise source.