The .asJSON expressions generally deal with the content of a data structure type of object (array, tiles, dictionary...).
The instance variables are part of the object type, not the content of the current instance of the object.
If you want to save the values of your instance variables, you would likely have to save them in addition to the .asJSON value, on their own.
You could serialize your own string.
For example:
myFullString = array.asJSON & "¤" & array.variable1 & "¤" & array.variable2
When you want to load the information from 'myFullString' into the array, you would use the tokenat() system expression.
array action load : tokenat(myFullString,0, "¤")
Set array instance variable : variable 1 = tokenat(myFullString,1,"¤")
Set array instance variable : variable 2 = tokenat(myFullString,2, "¤")
Here, the separator "¤" is a character that likely will not be used in the asJSON content and/or instance variable value.
If you want to save the state of an object, use the dedicated system action : construct.net/en/make-games/manuals/construct-3/system-reference/system-actions
This will save the content of your object, as well as its instance variables.