Apologies for a slight thread hijack, but I thought it makes more sense to put this here than start a new thread.
I had a similar issue with my 616 - in my case there was a 0.5mV (i.e. 50 count) discrepancy vs zero check and using an external short. This corresponds to 5pA leakage, which I believe is excessive for this instrument. In my case detaching the zero check relay had no effect. By swapping around the input FETs and thorough cleaning, I managed to reduce the leakage to to 2-3pA. I then had the bright idea of detaching the protection transistor to see how much it was contributing... aaaand it's dead.
Well, the FETs were toast but the op-amp was fine, so inspired by Alexander Nitkin's 617 fix, I replaced the FETs with one side of an LMC662. After this fix the leakage was below 1 count I.e. 100fA. I have some electrolytics to replace before buttoning it back up, but after that I'll see if I can use the charge measurement function to get a better idea of the remaining leakage.
Hope someone finds this useful!