Amplify voltage between transistors in a current mirror setup?
A typical way of amplifying the difference between two voltages is with an op-amp configuration known as a "differential amplifier".  A basic explanation is here:
http://hyperphysics.phy-astr.gsu.edu/hbase/Electronic/opampvar6.html

More information can be found on Wikipedia or in a circuits textbook.
https://en.wikipedia.org/wiki/Differential_amplifier

To add a differential amplifier to your circuit, I would first connect the source of each transistor to ground so they have the same \$V_S\$, the drain of each to its own identical current source, and connect the gates to the drain terminals (so that \$V_{GS}=V_{DS}\$, which will be determined by (1) the transistor geometry and materials, (2) the current source, and most importantly, (3) the radiation applied).  This is called a "diode" connection, but I believe it is what you have already built and measured, or will at least will work the same way.  I may be wrong here.  From here, you can connect the two gates to the inputs of the differential amplifier.  This schematic might be a good start (don't pay much attention to the component values, they're just placeholders):







simulate this circuit &ndash; Schematic created using CircuitLab

Two comments on your schematic diagrams, since they are unclear.  First, your N-channel MOSFETs are mislabeled.  You have swapped the source and drain terminals.  Second, the wires in your schematic connect to an odd portion of the MOSFET symbol.  See this picture for reference:
https://en.wikipedia.org/wiki/MOSFET#/media/File:IGFET_N-Ch_Enh_Labelled.svg
A schematic should only connect to the terminals of the MOSFET outside of the circled portion.

This is a cool application of a TFT, by the way.

EDIT:

The circuit I posted is very similar to a PTAT temperature sensor.  Figure 4 at https://www.analog.com/en/analog-dialogue/articles/chip-to-monitor-environmental-conditions-on-motherboard.html# provides a clear example:



In a PTAT sensor, either the two current sources are different, or they are the same and the transistor geometries are different.  This causes the two \$V_{BE}\$ voltages to respond differently with temperature changes.  Measuring this voltage difference allows you to calculate the absolute temperature.  If you can understand this principle, then you can see how your TFT radiation sensor works similarly.  Now that I think about it, I would be concerned that your voltage measurements at a fixed radiation exposure will also change with temperature.  You should confirm with environmental testing experiments.