My experience is that measuring voltages in a high resistance circuit is hardly as trivial as it seems first sight. And I've even seen intermittent changes of values of "precision" resistors randomly.
Why don't you try new resistors? You do not have to buy expensive precision parts for that experiment but select almost exact values from a dozen or so cheap 10%s. If the behavior of the instrument does not change you will know the resistors are not the cause of the problem.
Regards, Joe
Joe