Near-universally applicable alternative to "sanity check"

Consider, coherence check and confidence check.

coherence: systematic or logical connection or consistency M-W

consistency: agreement or harmony of parts or features to one another or a whole. M-W

confidence: faith or belief that one will act in a right, proper, or effective way M-W

I'll suggest a 'soundness' check, or 'soundness scan' if the check is superficial:

soundness, noun
The condition of being free from defects or flaws.

(soundness. (n.d.) American Heritage® Dictionary of the English Language, Fifth Edition. (2011). Retrieved October 24 2015 from http://www.thefreedictionary.com/soundness.)

Wikipedia offers the term smoke test as synonymous with sanity check for software testing.

For the record, I think sanity check is more recognizable and an acceptable phrase.

Perhaps you would prefer "health" to "sanity"?

Would "health check" pass your PC test of expressions that "should be avoided" "in the contest [sic] of software"? If not, maybe try the usual "quality control" or "quality assurance" testing.

[Sheesh. This is truly ridiculous. Health is a positive, and so is sanity. Anyone offended by use of the word sanity should ... (no, I didn't say have their head examined). Oh, and by the way, you won't find "sane" or "sanity" on the ableist language page you cited.]