Does increasing the current make a thermistor more accurate?
Running a thermistor with a typical resistance of 1k (somewhere in your range) with 30mA will mean it's developing 30V, or dissipating 1 watt. At 50mA, it will be 2.5 watts. 

This means it will be waaaay hotter than the ambient you're trying to measure at either current, and much further from your ambient at the higher current. Very inaccurate.

You only need a few volts swing.