In the phrase "beating obedient / to controlling hands" the word obedient is an adjective and thus should be modifying boat or heart, one of the earlier nouns. If it were the word beating that was meant to be modified by obedient then the word obediently should have been used.
In addition to the word beating giving an action to the heart it can also be giving an action to the boat (of line 418) because Eliot has not yet given us punctuation to terminate the line. In sailing terminology, to beat means to sail a boat against the wind (i.e., in the direction of the oncoming wind.)
Knowing now that beating could be the action of either the heart or the boat, which is it? Simarly, what is obedient, the heart or the boat or, despite the synyax, the beating?