I was also having other difficulties with the word kai in Matt 22:16:
This is excerpt from the verse given in Croy:
Διδάσκαλε, οἴδαμεν ὅτι ἀληθὴς εἶ καὶ τὴν ὁδὸν τοῦ θεοῦ ἐν ἀληθείᾳ διδάσκεις.
My attempt: O teacher, we know that you are true only if
you teach the way of God in truth.
New Oxford Annotated: Teacher, we know that you are sincere, and teach the way of God in accordance with truth...
KJV: Master, we know that thou art true, and teachest the way of God in truth...
My problem was taking εἶ καὶ as two separate words (εἶ - if, whether; καὶ - and, only, even). I looked in a few more Bibles, trying to find if anyone used my translation. That was not the case. Then, I got out the grammar:
εἶ καὶ commonly admits that a condition exists (granting that), but does not regard it as a hindrance. The condition, though it exists, is a matter of no moment so far as the statement in the principal clause is concerned. [Smyth, 2375]
And there is the problem with my translation--it emphasizes the condition, and makes the first clause is indeed dependent on the second.