That drawer looks like it's made out of polyethylene, so nominally very high resistivity. I made direct resistivity measurements on ABS (~2x10^15 ohms), which is also very high. The technique I had to use was specified in 60079-0, and it also shows up in other places. The basic idea:
1. Get a representative test sample. It could be the same material, or a material of known higher resistivity.
2. Use conductive paint to make two lines, 10 cm long, and 1 cm apart.
3. When dried, set up a power supply and ammeter to read the current. Note that while this test specifies up to 500V, you shouldn't need that because you are purposely making it conductive lower voltages should result in reasonable current readings. Measure for at least one minute.
4. The standard specifies that the surface shall be cleaned with distilled water, then isopropyl alcohol, then distilled water again. Also that it should be "conditioned" for 24 hours at less than 50% humidity.
5. The resistivity will then be 10 x V / I.
With multiple samples you could test:
A. Resistivity vs. number of coats.
B. Durability of coating vs. abrasion. Perhaps use the samples from test "A".