On a writing forum I visit, there is a discussion about eliminating certain words from a manuscript. But that reminds me of a discussion about grammar tricks, such as when to use who/whom, and inevitably someone suggests its best not to use tricks but to understand objects, subjects, and such to understand when to use which word.
I think the same must be done for eliminating "overused" words. You put the word there, and unless it was a pure error, it had a function. Understand the function of the word to make sure the replacement word has the exact same function and weight and still fits voice. Also pay attention to what happens if you revise the sentence into something else entirely, for you still have to understand the function the sentence was playing. In this case, if you intend a different function for the sentence, make sure it fits in the broader picture of paragraph, scene, voice, etc.
Basically, if content is king, I say context is queen. Make sure you pay attention to her too.
18 minutes ago