I'm not sure if I have understood your scenario correctly, but just for your information, if you are not aware of it yet, it's possible to define scenes as autoloaded singletons in the project settings, as well as pure script files. I have plenty of them in my project and my list of singletons is a mixed list of both .gd files and .tscn files.
The node name you give to the scene in the configuration will be the global name which you use in code to refer to the scene node.
And of course, the autoloaded scenes may contain exported variables.
For example, in my project, the scene:
"res://src/Core/Player.tscn"
containing the code:
extends Node
class_name Player
export (String) var starting_person_id
export (String) var starting_car_id
export (String) var starting_street_id
...
is setup in the AutoLoad tab with the Node Name:
"player"
and then exported variables as well as other members can be referred like:
player.starting_car_id
anywhere in the project code.
(Note that the node name "player" is in lowercase , deliberately to distinguish it from the class name "Player")