We were preapproved for a mortgage well exceeding what we want to spend on a home. We haven't locked in a rate yet but they are looking competetive. In addition, once we close, we can refinance the mortgage at a better rate with the same company at any point we want with no fees and minimal paperwork.

My question - is it worth the effort to shop for a better rate if we can adjust the current one for free?

Its always better to shop for a better rate. If you are patient and shop around you will save yourself the pain of re-financing later on. Good luck to you!