The correct phrase is most important, and the same goes for more important; they are often, if not always, shortened versions of what’s most important or what’s more important.
Importantly means in an important way, just as slowly means in a slow way. Using the full phrase what’s more importantly in a sentence illustrates the error well. What’s most importantly is that we try our best; this sentence doesn’t make sense. (Of course, it should be What’s most important is that….) It’s like saying What’s most clearly to us is that she’s trying her best; I’m sure it’s clear to everyone that the latter sentence is grammatically flawed, yet we give a pass to using importantly in the same way.
One on-line dictionary says that more important and more importantly are used in all kinds of text and by reputable writers, which means that there’s no reason not to use importantly.
Well, I can think of one reason: it’s wrong.
I agree that they are both used by reputable writers; however, I’ve said it before, and I’ll say it again: Writers aren’t necessarily grammarians, and many reputable writers and respected editors make some not-so-great grammar choices. Asserting that a particular usage is correct because famous writers or high-level editors use it defies logic; none of us knows everything.
I’ve seen editors print sentences such as These kind of ideas…. Does that mean that we should toss subject/verb agreement out the window? I’ve seen reputable writers use reason why. Does that mean that it’s not a redundancy? The answer to each question is, of course, no.