Hi,
Belive me, in normal conditions resistors above 1M should be treated with extreme care. Small contaminations with little moisture yield resistance under 1M so for me it looks quite possible you get swings of the measured signals! Of cource you can put 10M or 20M resistors but by paying extra care for the design (cascaded resistors, cuts in PCB under the resistors, ultrasonic cleaning of the PCB, usage of bigger footprint components, covering the resistors with epoxy, etc.)