The word "ausgenommen" just seems strange/wrong here. "Ausgesprochen", "ausnehmend" or "ausgesucht" would all be fitting, all basically meaning "especially", which is why I suspect that the speaker got his vocabulary mixed up and meant either of these. Which, of course, makes this a bad example for discussing its grammar.
That being said, the grammatical function is the same for all of them, they're used as attributes for the adjective "höflich". Their use is similar to qualifiers like "sehr" or "besonders".
Der Gast war sehr höflich.
Der Gast war besonders höflich.
Der Gast war ausgesprochen höflich. (The guest was extremely polite.)
Der ausgesprochen höfliche Gast zog beim Betreten der Wohnung sofort seine Schuhe aus.
"Ausgesprochen" has a special meaning as an adjective (= "extremely") that is completely detached from its existence as a participle of "aussprechen". "Ausgenommen" actually also has a side hustle as an adverb meaning "except for ...", but that's not what is meant in the sentence in the question, because in that function it always comes with an addition that says what is excepted.
In use as an attribute for another adjective, participles and adjectives aren't declined. In English, the adverbial form with -ly is used.
das scheinbar kleinste Haus der Straße (the seemingly smallest house)
das schreiend gelbe Haus (the glaringly yellow house)
das übertrieben dekorierte Haus (the exaggeratedly decorated house)
Modal particles like "aber", in contrast, qualify the whole statement of the sentence, not just an adjective.