All good but complex solutions.
What you're experiencing is gain error; you just failed to account for your 2.5V source's Thevenin impedance of 3.75k. If you don't use the 2.5V elsewhere, you just have to account for it.
Just reduce Rin on the (-) side of the op amp by 3.75k and the output will be as you expect. You'll have to calibrate it with the sensor output at 2.5V.
The other solution is to increase Rin and Rf. Is Rin currently about 4.0k? With sub-nanoampere bias and offset currents you should be able to increase Rin and Rf by a factor of twenty or more and reduce their influence on the 2.5V. You can still reduce the Rin on the (-) side by 3.75kΩ which should now be a small percentage.