There are two related issues that need to be addressed when correcting file permissions:
Actual file permissions (On Unix-like systems all files have an owner, a group, and a set of permissions intrinsic to them) and SMB/CIFS file permissions (the permissions given to users accessing the share). They're not the same, and whichever is more restrictive wins.
For example, if you configure the share to give read and write permissions to a given user, a user logging in will not necessarily have read and write permissions for all files if the files themselves have more restrictive permissions.
You won't be able to change the permissions on the windows PC through explorer in part because windows doesn't really "understand" Unix file permissions, but if you can log into your NAS somehow, you can change the permissions on the NAS. Does your NAS provide a terminal interface? Are you comfortable on the command line at all? I know nothing at all about commercial NAS's, but if you can get to a command line on the NAS I can offer some suggestions.
The short term "easy" fix is to chmod all the existing files to have global read-write permission, but that's not a great idea for security, and won't fix things going forward.
The long term (and better) fix is to create an access group, change all existing files to be owned by that group, include both your windows and Id users in that group, set the permissions correctly, and then set the directories to use the new access group by default in the future.