Wordwind, I have some trouble with your use of "integrated" as an adjectival form of "integrity."
Whilst both words derive from the Latininteger, in common use they have slightly different connotations, I think.
It's not too bad when you use integrated as an adjective to describe someone/thing's completeness or unity - although even here, it jars a bit - but when you use it to describe someone's, or some institution's, honesty, it doesn't fit at all.
Both Cambridge and MW agree that integrity can mean either unity or honesty, but that integrate only means unite or complete.

And a slightly belated welcome to Lori, and thanks for an interesting thread.