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Don't roll your own solution, use ScaNN (https://github.com/google-research/google-research/tree/master/scann) or Faiss (https://github.com/facebookresearch/faiss). I used the internal version of ScaNN while I was at Google, and found it incredibly well put-together. Can't speak to the open-source version, but it should be similarly good. These might be a bit overkill given your set sizes, but it'll be easier than building your own fix.
Don't roll your own solution, use ScaNN (https://github.com/google-research/google-research/tree/master/scann) or Faiss (https://github.com/facebookresearch/faiss). I used the internal version of ScaNN while I was at Google, and found it incredibly well put-together. Can't speak to the open-source version, but it should be similarly good. These might be a bit overkill given your set sizes, but it'll be easier than building your own fix.