But I was asked whether to stick with "cross," for example, if you've already used that several times-- isn't "traverse" better than repeating "cross"?
My thoughts-- repetition is not a tool of the devil. It's less of an evil than words that will stop the reader from reading to go look them up in a dictionary-- what happens to pacing then? Go with
the most RIGHT word, and the less it calls attention to itself the better-- but if the RIGHT word is something arcane and unusual, well, okay. But "traversed" rather than "crossed"? I'm just not sure that "traversed" is a good enough, evocative enough, beautiful enough word to waste a lot of time on. Do what feels right, but understand the implications of it.
Me, I wouldn't halt the flow of the narrative for a word like "traversed," but that's me. I think SENTENCES, not words particularly, should be made interesting, and sentences can aid or impede pacing and meaning.
What I'm trying to say is: If it works, it works. If you want to use the word traversed, go ahead. If it works, if it gives the reader a better experience (for example, in a more formal prose style, it might be le mot juste). I just wouldn't do it to avoid repeating "crossed". If I didn't want to repeat "crossed," I'd re-craft the whole sentence, because it's not just repetition of a word, it's repetition of an ACTION, and if the former is wrong, the latter is too. Words are great, but they are part of sentences, which are expressing action, thought, and feeling, and if the experience is repetitive, I probably have to change more than just the words. So I guess if the repetition of a word (especially a verb) bothers you enough, sticks out enough, what I'd suggest is that you go
back and see if you're repeating the ACTION too much.
For example, let's say I'm writing a letter, and I realize I have started almost every sentence with "I"-- I am doing this, I visited so and so, I'm feeling sad, I I I. Now the problem is not that every sentence starts with "I", and the solution isn't to invert the sentence order: "Barcelona was the last place I visited." The problem is that I'm obsessed with myself, and my narcissism and self-centeredness is showing in the paucity of my vocabulary. :) The solution is to go back and rewrite the letter to be more of a conversation than a press release-- to at least pretend as I write that I care about the recipient of the letter and, actually, the whole rest of the world that isn't "I".
That is, repetition of a word might indicate repetition of a far more dastardly sort. (Remember that old joke? "But enough about me! Let's talk about you! So... don't you think I'm fabulous?"
Sentences are about their meaning, not about their words. So if your words are repeating, use that as a clue to find out what else is repeating, what deeper is repeating. And see if you need to transform THAT into something fresher, and the words will be fresher too.
So-- be thinking of wording and sentence problems as perhaps being symptoms of something being wrong with your scene or story. If there's a passage with boring, vague terminology and sentences, that could be because the passage itself, the action, the thought, the viewpoint, are boring. And you can't fix that problem by fixing the words... but fixing the underlying problem will probably lead you to a more vibrant expression and wording.