Measuring Cu2O Thickness in Oxidized Copper Sheet
I like your idea to follow up the oxidation of metallic copper by analysing a by means of X rays. If you find a way to obtain a nice cross-section of your plates, I would suggest to analyse them however by means of EDX, where electron beams are used to excite the material locally, which relaxes by the emission of X rays of characteristic energy.  This will offer you both a qualitative, as well as a quantitative characterisation of your sample.  Monitoring corrosion is a recurrent task (cf. here) for this technique, recording concentration profiles, too.
In the easiest case imaginable, your scan trace would simply recognise &quot;high level&quot; (for pure copper), &quot;low level&quot; (for the adlayer of $\ce{Cu2O}$, lowered because of the presence of oxygen) and &quot;background level&quot; (around your plate, practically equal to zero), as schematically depicted in the following drawing.  Assuming you follow the concentration of copper as indicator, the higher the concentration of copper, the higher the read-out signal (the intensity of the $K_\alpha{}$ X-ray generated):

You mentioned the layer of $\ce{Cu2O}$ is not homogeneous, likely contains grains of unreacted copper.  Tentatively I tried to depict this situation in the following drawing, where the darker polka dots are meant to be representative for remaining starting material:

You may, depending on the scan trace chosen, encounter earlier or later such a grain.  Depending on the relative size of this grain, the beam diameter, the distance towards the pure copper matrix, the read-out signal will be influenced more, or less; hence the attenuation of the signal likely will not be as smooth as idealised here. Yet while scanning along the $x$-direction, it is possible to record $i$) $x_1$ when the high-level read-out decreases, and $ii$) $x_2$ when you reach the surface of the mixture of $\ce{Cu2O}$ and $\ce{Cu}$ towards the vacuum chamber, and hence to measure the thickness of the oxide layer.