What is the best database design to keep track of fields with multiple values?
Your new design constraint is such that there's a many-to-many relationship between pages and fields, and a many-to-many relationship between page-fields and field values.  That means you'd have to do this:

Page
* Page_Id

Field
* Field_Id
* Field_Type_Id
* Field_Name

Page_Field
* Page_Field_ID
* Page_Id
* Field_Id

Page_Field_FieldValue
* Page_Field_FieldValue_ID
* Page_Field_ID
* FieldValue_Id

FieldValue
* FieldValue_Id
* FieldValue_Value
* Current_Value


"That's really gross" you're thinking.  Yes, it is.  I'd strongly suggest creating views (indexed or materialized if possible) to make retrieval easier.  It doesn't really solve your problem of having to define everything for each new page, but at least you won't be storing the same data repeatedly.

The Field_Type table doesn't change at all.  It's relation to Field is the same.  I did not list it in order to reduce confusion.

I'd also caution about using the FieldValue.Current_Value field as you seem to be suggesting, as that will not really work if your application allows multiple users.  Application state needs to be stored separately from application data, typically.