Hi Reigningfear,
This is not exactly how it works. The user would need to have write permissions to the record to be able to save it, assigning field level permissions to the user does not elevate them to have the ability to write the record and only those two fields.
You would need to do the following if you want to accomplish this:
1. Provide role with security to update the records to the users
2. Enable field level security on all fields that you would want to update on the record (overall) by any of the users
3. Setup two field security profiles with one assigned to all the users that will update everything and these will have "Yes" for create, read, update and the 2nd profile for the restricted users that will have only read for most fields and update for the ones you allow them to change.
Thanks,