git cherry-pick

Quick and dirty guide:

Checkout the branch you want to merge your work into
Create a new fresh branch off of that. Something like merge/featurename
Open the GitHub.com PR screen and open the PR screen for the branch your work is on and copy the hashes for the commits you want to cherry-pick
Run git cherry-pick [hash] for each of the commits, in historical order
Open a PR for merge/featurename into the branch you want to merge your work into