Creating a small range, small baseline varying resistor
A simple option is to put 101 ohms in parallel with the 10 k resistor. Then the net resistance is 100 ohms. If the 10k rose to 110k the resistance only becomes 100.9 ohms i.e. a change of 0.9 ohm sat on top of a base of 100 ohm.

If the change needs to be 3 ohms then choose a resistor higher than 101 ohms (say) 330 ohms for a guess. Now the base resistance is 319.45 ohms and rises to  329 ohms, a change of about ten ohms.

You can do the calculations yourself and maybe choose a value of 150 ohms: the result is a resistor that varies from 147.8 ohms to 149.8 ohms.

Given tolerances and that expectations are sometimes more flexible after a little thinking, does this offer a solution?

I still think this is an XY problem.