You can buy your rights back from some big-name journals. My last big paper was in a hybrid journal with a high impact factor (Molecular Psychiatry) for which we paid to have a CC BY license (fortunately, TAA was willing to pay the $4,000 fee). 
Finally, you can read elsewhere about green open access (self-archiving, sometimes after a delay). The SHERPA/RoMEO database is a great first stop to identify journal policies on preprints, self-archiving of the submitted manuscript, and posting final papers to the web. Many of these options do not preserve your right to re-use your own words and data, but they at least help make your work more widely available. Doing so is not only nice to others, including patients and third-world docs, it also tends to boost citations of the article.

Conclusion

So, even if you feel you have to give your work away to a high-JIF journal, you do have alternatives. Give them a try!