Learn English – Adverbial form of “scrutiny”

You can certainly use deeper as the comparative of the adverb deep. It was good enough for Milton (‘That they may stumble on, and deeper fall’), and for other writers too.

That said, the sentence as a whole doesn’t sound quite right. For one thing, it's unusual to follow wisdom of with a noun in that way, rather than with the -ing form of a verb.

Just because a term does not appear in this or that dictionary does not make it “not a word”. For one thing, the “Free Dictionary” falls short of being an accepted standard in the English language.

But for another, productive affixes like un- and -ly can be applied to virtually any word from the target class to produce a perfectly viable new word. So even if you were using a little dictionary that happened to be missing an headword for something like unceremoniously, no one would ever question it if you used it.

So with your particular case of

• communicate > communication
• communication > communicational
• communicational > communicationally

you certainly you could do so. However, whether you should be creating such septasyllabic monsters is something else again; you might well want to use a longer phrase here instead.

You could just say they don’t communicate well, or that they’re poor communicators. All those, and many others, seem an improvement over the ponderous communicationally challenged.