Normally you build on the current application and Mendix will allow you to read data from both old and new entities.
I would take the existing application. Import the new application (modules) and make sure no conflicting names are used.
Reroute the roles, startpages and Menus.
After that write some batch-processing microflow to convert the data to the new structure.
Hide the old UI form the end-user. Maybe the Admin can still see it for checks.
In the end clear the old entities, but wait couple of weeks with that.
Has the new environment the same model as the old environment? Because then the restore of the backup should just work. Can you elaborate on what did go wrong? Otherwise create a support ticket so that Mendix does the transfer of the data. We did this a couple of times. We had a lot of file storage so it would take us way to much time to download and upload again. Mendix can do that way faster on their end.