I do have a complete other idea I would like to share here.
I think the biggest problem you are facing that you try to do something where the basic dropdown menu is not build for. Normally you choose from the options shown in the drop down menu and not a possibility to select “All”.
Therefore, you can build your own drop-down menu where you add a special “All”.
Here is one way how I did it in other applications:
The value of “All” is not saved as an option set or as data somewhere. Therefore, you don’t need to worry that is gonna be displayed somewhere.
I implemented in a way that you select “All” all listed options are being selected.
Is this helpful for you?