My knowledge of CRI is just based on reading stuff readily available on the internet, so that doesn’t make me an expert, just makes me a novice who did a lot of reading maybe ten years ago before purchasing two CRI 92 D65 fluorescents for my tabletop photo studio (since then I replaced those fixtures by more flexible light boxes and spot lights, but that’s irrelevant to the current discussion).
My “takeaway” point from all the reading was that CRI 92 was pretty much a minimum “good CRI” for photography, 95 is really good, and that anything under 90 was not good - the “goodness” scale - new technical term I just made up 
- isn’t linear, declines rapidly as the CRI numbers go down. Perhaps @chris can comment on the question of CRI numbers (see Using Hald CLUT to modify CRI of light source? - #3 by chris). Point of suspicion regarding these numbers: I find it somewhat suspiciously convenient that the highest CRI fluorescent then available locally (in a specialty lighting store, not in regular stores) had the magical 92 CRI. Maybe published “good enough” figures go up as the commercially available maximum CRI goes up. But from experience I’ll confirm that CRI 85 LED bulbs make awful lighting for taking photographs.
I’m guessing that research is like photography in the sense that if we all sat around waiting until we had the best possible equipment none of us would get anything done. I’m hoping that a good thing that results from this long thread is that you’ll have a working understanding of limitations on accuracy of the data you collect, which of course all data has limitations. The important thing - as I’m guessing you are already very well aware - is to try to figure out what those limitations on the data actually are, and try to provide checks and estimates of error where possible. You have access to a portable colorimeter, so that’s one available check.
Another check is to make a target shot of your Spyder Checkr 24 and go ahead and make a matrix profile. As @gwgill said, there’s just not enough color patches on this target chart to make a LUT profile, and probably not even a shaper matrix profile, but rather just make an “-am” matrix profile. It would be interesting to compare the deltas from the specified LAB values in the SpyderCheckr reference file, to results from your custom camera input profile vs results from the standard default matrix supplied by dcraw, which matrix profile is also available through the various free/libre raw processors.
Another check is to put a solid uniform gray piece of paper or better yet maybe a sheet of white or gray PVC plastic in the space where the product will be, and photograph this blank surface to get an idea of how uniform the lighting actually is and whether there are any hot spots from glare.
@afre raised an interesting question regarding the color of oranges vs LAB and vs taking photographs with a camera. I did some rudimentary checking using a photograph of an orange that I made earlier this year - oddly enough my goal was to get an idea of the LAB values of an orange - I was painting a picture of an orange and wanted an idea of “how orange is an orange”. I also checked the orange photograph’s LAB values against a photograph of an IT8 target chart - some cameras have trouble with high chroma yellow and orange has a lot of yellow in it, but I think actual oranges have a low enough chroma to not wander into the problem areas for camera matrix input profiles. I’ll post images and results in a bit.