bend over backwards vs conduct

bend over backwards is not a noun while conduct is a noun.

Word	Noun	Adjective	Verb	Adverb
bend over backwards	No	No	Yes	No
conduct	Yes	No	Yes	No

As verbs, conduct is a hypernym of bend over backwards; that is, conduct is a word with a broader meaning than bend over backwards:

bend over backwards: try very hard to please someone
conduct: behave in a certain manner; show a certain behavior; conduct or comport oneself

Other hypernyms of bend over backwards include acquit, act, bear, behave, carry, comport, deport, do.

bend over backwards (noun)	conduct (noun)
	manner of acting or controlling yourself
	(behavioral attributes) the way a person behaves toward other people

bend over backwards (verb)	conduct (verb)
try very hard to please someone	behave in a certain manner; show a certain behavior; conduct or comport oneself
	lead, as in the performance of a composition
	lead musicians in the performance of
	transmit or serve as the medium for transmission
	take somebody somewhere
	direct the course of; manage or control