So the solution was to create a new ServiceProvider.
This solution works for Override
php artisan make:provider MyServiceProvider
Which extended the Vendor service provider (found within config/app.php). Within that ServiceProvider, add my alias within the overridden register method
$loader->alias('Vendor\VendorName\Class', 'App\Vendor\MyCustomClass');
https://stackoverflow.com/a/47926486/10589868
Now, how do I extend the overridden class? I tried this:
$loader->alias('ClassParent', 'Vendor\VendorName\Class');
$loader->alias('Vendor\VendorName\Class', 'App\Vendor\MyCustomClass');
...
class MyCustomClass extends ClassParent {} // not working