The override field level permissions only work if the source fields are in the same table. If the users do not have access to those fields in other tables, then you wont be able to use the Override permissions method. You may need to open those fields with access and limit the access for those users to those fields in other ways like with form rules and hiding the tables.
I don't really have a great suggestion but I don't know the specifics of your app and what wiggle room we have.
------------------------------
Mark Shnier (YQC)
mark.shnier@gmail.com
------------------------------
