Hi Martin,
very good Video, keep them coming.
You got yourself a very nice meter.
In case you not aware here the link to the HP Journal Issue from 1986. Page 15 covering the HP3457A how it works and so on
Multimeter Review / buyers guide: Part 2 - HP 3457A There is also a HP Journal with an big article about the 3458A 8,5Digit Meter if you interested.
The Service Manual including the schematics can be found here
http://www.home.agilent.com/agilent/techSupport.jspx?pid=3457A:epsg:pro&pageMode=MN&lc=eng&cc=USNoisey Digits and PLCs:
In my opinion the main source off the noise in the reading comes is your power supply, try a battery the reading should be more stable.
The ADCs in this meter are Multislope ADCs (see also Dualslope ADC); the reason why they use powerline cycles for measurement aperture is that, at least in theory, with this type of ADCs, the error from the positive halfwave and the negative should cancel each other out perfectly.
And a multiple number of PLC is of course used too average the result.
