Has meloxicam / mobic ever been known to cause anxiety?

Yes, Meloxicam can cause nervous system adverse reactions, as per product labeling, most of the time is less than 2 %, including Anxiety, Depression, Nervousness, Abnormal Dreams, Insomnia and many more. May be you can switch it to Tylenol (Acetaminophen) 650 mg for pain instead of NSAIDs, but sometimes Tylenol can cause Anxiety too but it is very rare.

Anxiety would be uncommon as a side effect for meloxicam, still described with an estimated incidence of less than 2%.