In order to enter data in the table, your managers would need Read and Write access to the file containing that table. That access applies to the whole document, not just the table that is the form.
The only way I see to get what you want is to place the table/form OR the field(s) you do not want the managers to have access to in a second document, then set permissions of each file to give them read-write access to only the file in which they are to record the end of shift data.
Transferring that data to the main document would then require either copy and paste or use of an AppleScript by you or someone with read-write access to both files.
Regards,
Barry