For local testing of frontend code there is usually no need for building/publishing the visual studio solution. For your local dev environment, you have several options that will be a lot faster:
A) Symlink from Frontend build-dir to webroot
Set up a symbolic link in the local webroot and point that directory to the output of the frontend build. With ...
You need to review the coveo search config files and make copies of QA index definitions and name them with "DEV_" prefix so you know. Once you define for all databases (master, web, core) you should see these new index definitions in the index manager in sitecore control panel. Select only these indexes (prefix "DEV_") and index them.