I got to thinking I could answer my own questions by browsing the Internet.
With the help of Google, I concluded that there really isn't an answer that everyone agrees on when it comes to this construction.
From:
[link]
The final factor is the traditional use of Latin grammatical concepts to teach English grammar. This historical quirk dates to the 17th century, and has never quite left us. From this we get the Latin-derived rule, which Fowler still acknowledges. And we *do* follow that rule to some extent:
"Who are they?" (not "Who are them?" or "Whom are they?")
"We are they!" (in response to the preceding)
"It is I who am at fault."
"That's the man who he is."
But not always. "It is me" is attested since the 16th Century. (Speakers who would substitute "me" for "I" in the "It is I who am at fault" example would also sacrifice the agreement of person, and substitute "is" for "am" [resulting in "It is me who is at fault"].
-----
From:
[link]
It is I who have allergies.
- IT is the subject of the independent clause. I is the predicate nominative to IT. WHO is the subject of the final dependent clause.
------
From these excerpts I conclude that "It is I who am ..." is the more conservative form, "...I who is ..." being more modern.
Actual usage - from my Internet sample - whether right or wrong, varies between "It is I who have/am" and "It is I who has/is".
I wasn't interested enough in doing a count! I leave that to the reader! It seemed about 50-50, actually.