Initial Full Backup required for Filegroup Backups?
I think what you're looking for is PARTIAL backups, which backup read/write filegroups (including PRIMARY) and any specified read-only filegroups. For your requirement, you could perform a PARTIAL backup of the 4 read/write filegroups plus PRIMARY and a File Backup of the 8 read-only filegroups.

Your file backups would not need to be performed again unless A) you change them to read/write, or B) your file backups become damaged. Beyond that, the file backups can be used for any restore going forward as needed.

Your PARTIAL backup of the PRIMARY and read-write filegroups can then be used as the source for PARTIAL restores or as a differential base for DIFFERENTIAL PARTIAL backups.

NOTE: The PRIMARY filegroup contains system tables and database metadata, including metadata about the state of other database files/filegroups, so you should always include this in your regular backup processes, it can't be backed up once and retained for future reference like the read-only filegroups. If you've designed your database correctly, you would ideally have little to no user data in the PRIMARY filegroup anyway, so its includion in PARTIAL backups shouldn't make much difference to performance or space consumption.

EDIT:

As per Peter's comment, I wanted to include a quote from the documentation:


  Partial backups are useful whenever you want to exclude read-only
  filegroups. A partial backup resembles a full database backup, but a
  partial backup does not contain all the filegroups. Instead, for a
  read-write database, a partial backup contains the data in the primary
  filegroup, every read-write filegroup, and, optionally, one or more
  read-only files. A partial backup of a read-only database contains
  only the primary filegroup.


So with a PARTIAL backup, you're backing up all read/write filegroups, including PRIMARY, without exception. It is possible to include read-only files or filegroups as well, but all read/write are included in a PARTIAL backup automatically.