I would have no idea what this "ground" is you describe. What I see are a bunch of antennas. Are you using 1.0? It's very possible for what you are showing in this video that it would make a difference as it appears the filter has a lower cutoff.
Personally, I would not have all this added wire, BT off, twisted the test leads, rev 1.0. Then again, you can see what I am doing to make this same measurement.
Ground is what in England I would call "earth". It is the protective safety ground in my house, the third wire in power outlets. Since you suggested that static charge might be a cause I was trying to eliminate it by earthing all parts of the apparatus including myself.
Please do not be distracted by the long test leads. The effect is observed whether test leads are plugged in or not. I do not have your lab facilities with anti-static mats, banana-to-coax adapters, shielded coax, fabricated widgets with shielding or any of that stuff. If all of that is a prerequisite for using a DMM then few people going to be able to use a DMM.
Also I am using the latest firmware as published. I do not see any point an backtracking to v1.0 as that is now long superseded and has problems of its own.
Finally, I will say again, this effect happens merely by touching the Hold button. The meter can be in any location, in any orientation, with or without test leads plugged in (for example it happens measuring temperature with a thermocouple).
If I had to guess at a cause, I would say the meter is somehow responding to capacitance between my finger and the button (or whatever is behind the button).
I have observed a similar problem when pressing the Rel button. Upon releasing the button the reading jumps, rendering the Rel action useless as it locks in the "jumped" value rather than the original value. I have tried to avoid this jumping of the reading by using a conductive or non-conductive push stick instead of my finger. However neither eliminated the problem, it still jumped even when using a plastic pen to push the button.