I have my doubts about the ESP diagnostic too. On both my printers the ESP check ends in an error but both calibration and profiling goes well for papers. It is possible that HP considers other factors than the spectrometer condition too in that diagnose.
That said I never profile canvas on the machine itself but use an Eye 1 Pro for the task. For more reasons, my profiling is done with the varnish applied and that is simply more difficult in handling on the printers and my best guess the printer's spectrometer is not really up to that task either, read further on. When I replaced belts on both machines and a head carriage board on the Z3200 there was time to check the spectrometer part too for the sliding door and the optics. I did not see problems there. On the inside of the sliding door there must be a white calibration patch and that could have changed properties but I did not take that one out in fear of breaking the part. Replacing the spectrometer part is not difficult when you ever have done a belt replacement, I think you can not access that part without removing the head carriage from the printer.
Essentially the Z's spectrometer is more like the Isis or Munki one. A white LED is used as I understand it and the Eye 1 Pro uses a tungsten lamp. I also think ( based on the cleaning of the parts) that where the Eye 1 Pro has lighting in a 45° cone shape, the Z spectro has a single light source point at 45°. A lot can be compensated by multiple readings per patch on an irregular texture but not all, the more when the irregular surface is varnished and has some regular pattern like in canvas. I know the spectrometer is allowed to make longer readings on dark patches and given the large size of the individual patches multiple readings should be easy but it is still not ideal.
If your measurements are alright for papers then I would not go the route of replacing the color sensor but get a separate colori- or spectrometer that can make good profiles on canvas. Averaging some measurements is even then a good approach as canvas can be tricky. Measuring of fabrics is often done with spectrometers that have a wider sensor opening, an Ulbricht sphere lighting improves on that. I do not know whether the Color Munki can average with its normal software but it must possible with ArgyllCMS. The iterative system of the normal X-rite software is not ideal either for canvas in my (theoretical :-) opinion, for the reasons sketched above, building extra information with a second measurement on top of the first one is good when both measurements are consistent, hard to get that condition on canvas. It will ask for a much longer process too as the second target has to be made (including varnishing) with the information from the first measurements.
Met vriendelijke groet, Ernsthttp://www.pigment-print.com/spectralplots/spectrumviz_1.htm
December 2012, 500+ inkjet media white spectral plots.