everyone permissions

I have created a new SMB share as the ReadyNas documentation has suggested.

Created the share on Readynas, set everyone with R/W, and disable anonymous access.

From a Windows server open the \\readynas\share_Name, right click select permissions. Add the permissions I want, domain admins with r/w.

When trying to write to the folder with a windows service account added to the domain admins group, it errors with Access denied. If I add the "everyone" into the nt permissions with full r/w access the service account can wright to the share w/o issue.

I do not want everyone to be able to open the share and access data.

Is it possible to remove windows "everyone" and still wright data with a user belonging to the domain admins group?