You need to reconsider the metaphor you are using.
You've chosen "Allow diagonal" and "Force horizontal" which is a difficult dichotomy to handle. The two terms don't directly communicate two different states of a single value. With these terms it's going to be difficult for anyone to figure out what state a filled or empty checkbox ...
I've seen this situation very often and the regular approach is a checkbox button beside the title with two actions:
Select all the items below this title
Unselect all the items below this title
and one info state:
This title has some selected items
About the submit button at the bottom usually has the functionality that forces the user to read all the ...
Just to offer an alternative suggestion (not saying this one is necessarily better).
The one concern of having "None" as a drop down value is how obvious it is that it's an option that the user will be able to find in the list. Having it as the default selected option does help to resolve this issue, although it isn't as obvious how to revert to &...
With the checkbox you basically break it up into two questions:
Are there any extracurricular activities involved?
If yes; What extracurricular activities are involved?
But you have already simplified it to one question:
(What) Extracurricular activities (are) involved(?)
The answer might as well be "None", just like any other option in the ...