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I don't know how it could be easier: You position inside a word anywhere, press CMD+OPTION+G; the next word is already selected, you can already edit it, no need to bring up Find panel.

This does seem to work but its pretty painful key combination on my mac keyboard.

Or double-tap Command+D.

This doesn't seem to work well as it highlights multiple instances of the word I was on. The current instance and the next instance(but not all instances).

cmd + e will mark the current selection (or current word if there's no selection), cmd + g (or cmd + shift + g to go backwards) will find other instances of it. ctrl + cmd + g will find all instances of the current word, which you can edit simultaneously.

For that use-case, isn't control-d / cmd-d pretty quick?

Not just you. Sublime's find is anything but.