You wouldn't hear someone say: "But more important, I'm always right."
They would say: "But more importantly, I'm always right."
When I hear "more importantly", I think of it being employed in an example like this.
I have heard it said (and written) that way.
That's why I asked.
And then I found this...
"The adverbial construction "more importantly"
is trying to modify a verb within the main part of the sentence,
which isn't appropriate. "More important" will suffice —
or consider leaving it out altogether.
(For the same reason, when enumerating causes,
say, we'd write "third" instead of "thirdly.")"
Perhaps it how one uses it...