Actually I think there is a database called “wordnet” that you might be able to parse through in this way. You would be looking for words that only have one sense, and are a synonym with another word that only has one sense. Then you could build a list if all the words that are this way, and it would probably be perfectly fine to pretend that they are the same word for the sake of an index.

Now I’m curious as to how many words there are like this. That should be a pretty straightforward programming project.