You are under a misapprension - the internal "pull-up resistors" on the chip are probably FETs with a long thin channel that behaves roughly like a high value resistance, but won't be very linear. To fab an actual resistor on silicon takes a lot more chip real estate than a FET, and is only done when necessary such as in analog opamps.
There is a single transistor current limiter that is Very predictable and compliant when used at 1 to 5 % of it's collector current. I'd use that circuit for a programmable current generator and measure the voltage across the test resistor generated by this CC gen with the internal 1.1 Vrf. It sounds complicated but it is a couple of transistors or gates to shift the CC gen output range or a DAC to program the CC gen. The circuit will work with the minimum to the max where the A/D Vref is gated or a DAC under program control establishes a known current then measures the voltage to determine the unknown 'resistance'. The point is that this can magnify the basic 10 bit res by quite a bit without so very much complicated or arcane op-amp things. Really interestiing things even with limited pin count applications.Bob