Attiny85 - Method to discard glitched ADC values?
I have no idea why they haven't used a fixed pull-up, but the pull-up
  is only done when the controller wants to read the sensor for only
  about 120us.


If you want to get a good resolution in the resistance measurement, the
resistance of your pull-up should be in the same range as the resistance
of your sensor. If your sensors have low resistance, this means the
voltage divider will draw significant current. In order to save energy,
it makes sense to power the voltage divider only while you are doing the
measurement.


  the reading window is really small (100-120us).


That's short indeed. If you analogRead() a single channel in a tight
loop, you will get one reading every 108.6&nbsp;µs (128×14&nbsp;CPU
cycles ÷&nbsp;16.5&nbsp;MHz), and you have a small risk of missing the
window. If you are reading two channels, then you have about 50% risk of
missing the window.

Here is what I would do:


Set the ADC prescaler to 64 instead of 128. This way you will get one
reading roughly every 54&nbsp;µs, and at least one sample (but more
often two) during the reading window.
Read a single channel in a tight loop, until you get a value above
your minimum. Then take one more reading and use the largest of the
two as your “good” value.
Switch to the other channel and go back to step 2.


This assumes that outside the reading window your ADC input reads close
to zero, as it is grounded through the sensor, with no pull-up. You then
have, on each channel, a train of positive pulses, and you want to
measure the height of those pulses. There is a small risk of you
sampling the rising edge of a pulse, which could give a wrong value
which is nevertheless above your minimum. If this happens, then the next
sample will be near the center of the pulse. That's why I recommend
taking one extra sample and using the largest of the two.