IC7 is an old 4053 CMOS switch chip. The selected is probably checking for low leakage. These low cost parts are not checked very much at production. So the maximum leakage current can be quite high though the typical leakage current is rather low (e.g. 10 pA range). The circuit may like to have a reasonable low leakage, like no more than 100 pA. If the leakage is OK, it should not effect the accuracy / calibration very much. The problem is more that the old part may have had leakage during the last calibration. In this case even a perfect replacement can have an effect.
However to me it looks odd to have a problem with negative signals only if IC7 is bad. It would have to be a rather odd failure to cause an error with negative voltages only. There are quite a few other chips / transistors that are more likely to cause such a failure.
Is the main amplifier / buffer still working ? The signal at the output of IC40 should be a really good test point.
Not very good, but as a try to preserve the calibration, one could try to measure the 6.95 reference directly with the meter in the hope the positive reading is still OK and accurate. The 200 mV signal at R107 (only the positive side) could be another reference point.
The circuit diagram shows a few odd points around LM324 with massive capacitive load - normally a sure reason for trouble
. There may be so extra caps not in the plan.