This plugin allows you to easily modify the REST API URL Prefix in your WordPress installation in a simple and failproof way.
To install the plugin, download the 'Custom-REST-API-URL-Prefix.php' file and upload it to the 'plugins' folder in your WordPress directory. Then, go to the plugins page in your WordPress dashboard to activate it. Everything as usual.
Another option is to upload it to 'mu-plugins' folder, which is a good idea for this kind of functionality.
You can configure the plugin options under the 'Settings' menu.