Hi,
With a quick inspection it appears that all the resistors are 1 percent tolerance. These resistors set the gain and offset so it could just be that one or more of the resistors are not correct even though they are still within their package stamped tolerance.
1 percent of 1.000 is 10mv, so adding that we get 1.010 volts, which is more than what you are seeing so it is very likely that there is a natural mismatch in the resistors somewhere.
To fix this you'd have to find out which resistor can be changed such that you get the same gain but a more accurate offset. This could probably be accomplished by paralleling another 1 percent resistor (of higher value) with one of the resistors and thus bringing down the total resistance by a small amount (probably around 0.3 percent).
As an approximation, to bring a 100k resistor value down by 1 percent we'd have to place a 10 Meg resistor in parallel with it. To bring it down by 0.3 percent we'd have to go three times higher, to 30 Meg. That would drop the resistance by roughly 0.3 percent.
I mention paralleling because that's easier to do, but you may have to go in series because 30M resistors might be hard to find for example. In series, you simply add 1 percent of the resistor value, or in this case, 0.3 percent, which would be 300 ohms for a 100k resistor.
I dont recommend using a pot except as a trial and error method which later to be replaced by a fixed resistor of the same makeup and tolerance.
This is assuming you dont use the circuit for what you call the 'passive' mode and you do use the circuit for what you call the 'active' mode. If this is not true, then you'll have to show the switching for going from passive to active so we can see what exactly changes that is supposed to change so we can analyze what is changing that is not supposed to change. We're only seeing part of the circuit right now so it's hard to tell.