That is common with sensitive high impedance circuits. Vibrating wires cause movement of charge. Mechanically securing the parts and wires helps.
I would tap around with an insulated poker or something to see if any areas are more sensitive than others.
I have 6 electrometers of different vendors including second K617 and non of them is doing that. There is some drift when you shake the device but just a little.
The one I have issues with, goes to higher range even from lightly knocking on the housing.
Anyway, I was able to remove old reed switches from the relays. Some are easily sliding out, some require desoldering the relay and poling the switch with tweezers.
Replaced only first 4 relays and now input current goes to 5fA in 5-10 seconds after switching to amps. Easily can be compensated to zero current.
The original look of the board was preserved.