Can I create a policy to disable a computer or user at a certain time?

Windows domain.
We close at 5.
I've been asked to disable certain computers/users at 5:15.

I know how to restrict access to the file system on the hour, but
a) that doesn't give enough grace time or too much, and
b) doesn't restrict enough, it only cripples

No, but you can allow users to log on only during certain hours; the setting is in the user account properties in Active Directory:

You can also use a GPO to force users to disconnect if they are logged in when their logon window expires.

Update about granularity:

According to this discussion, the Active Directory attribute which stores this settings doesn't allow for more than single-hour granularity, so it's not possible to specify lesser periods such as 15 or 30 mins, regardless of which tool you use to set it.