Currently, when you want to use the Media Module in Adobe DTM, the only way is to switch the AppMeasurement Core Code to "Custom" and paste the Media Module before the existing code. By doing so, you loose the option to one-click-upgrade via dropdown, and the ability to see if your property is using the Most Recent AppMeasurement code version or not.
I suggest to add a checkbox that is called "Add Media Module Core Code" to avoid the disadvantages and lets you work close to Adobe's best practice (see screenshot attached).