In FileMaker you can use Manage | Security to control access to records on a record by record basis but not fields. One option is to place the projections field(s) in a related table (can be related in a 1 to 1 relationship) so that record level access control can limit access to these fields depending on a value in a field that can be set by clicking the button.
See "Editing record access privileges" in FileMaker Help and check out this particular sub section: "Entering a formula for limiting access on a record-by-record basis" for a detailed description of how to set this up.
If you don't choose to go that route, you can add a validation rule on the field that rejects all changes to the projection field unless another "lock" field has a specified value. IsEmpty (LockField) is all you need for that. Your button can run a script to assign a value to this field and then further edits are no longer permitted.
You can also use script triggers that check the status of such a lock field and deny access to the field if the lock field is set to a value.