One way to approach this is to create a separate folder (that is not on the Matlab path) for your project.
When you set the Matlab working directory to this folder, Matlab should search this folder first, before anything else on the Matlab path, and it will find the locally-defined functions first.
Another approach is to manage the Matlab search path by adding the folder that contains these functions to the beginning of the search path. Matlab will find them first.
This second approach requires you to un-do the path assignment when you are running other projects, so you have to be careful. You can use setup scripts to manage the path changes.