So I'm getting close to having the site fully built out, and some days had passed since I'd fiddled with the site's settings (took a couple days off for the holidays).
On returning to it, I decided I needed a new site category. Added it without difficulty.
Created a new site using the new category. No increment in the new category.
Created a new site using a previously existing category. Increment successful.
Deleted test site. Decrement successful.
Created test site using existing category = increment successful.
Change category of test site from one (old) category to another (old) category. Decrement/increment successful.
Change category of test site to newly created category = no increment (tho the count DID decrement from the category no longer in use).
Deactivated/reactivated plugin = no change...new category is not recognized.