Dual Digital Pot With Different Op amps & Layout
How big a deal is it if the pots are far from the op amp feedback
  loops?


1) A very big issue. But keep the traces together and avoid digital traces. Cross them at a 90 deg angle if you have to. A 5pf to 22pf capacitor across the output and (-) input of the op-amps will stabilize them if you get ringing or parasitic oscillation in the op-amps.


  The voltages ultimately feed into 12-bit ADCs, so with the resolution
  being relatively low, can I get away with this as is?


2) A 12 bit ADC has a resolution of about 4,000:1, so unless some IC is oscillating or you need more decoupling capacitors the ADC should be quiet. Noise levels up to 1/2 LSB are OK and actually prevent the ADC from 'bit locking' due to lack of a signal.


  How do the SPI lines affect the DC analog readings if at all?


3) If not isolated by a dedicated ground shield, it is always best to run digital signals at right angles to analog signals. You do NOT want analog and digital lines running close and parallel, as it acts like 2 antennas close together and a good deal of digital noise could be imposed on your analog signals.4)  Pay attention to the basic rules, as you seem to be already doing, and the circuit should work just fine. By that I mean that any 'fine-tuning' or 'trimming' of values will be easy to do to get the best possible performance.