How do I use (O365) Exchange Online custom attributes (1 to 15) when I have directory sync enabled and no exchange installed on-premises?

It looks like Office 365 does not have the required editor, only on-premises Exchange does for the moment.

The official advice is to connect Windows PowerShell to the Exchange Online service and use it to modify the Exchange Custom Attributes by a command such as:

Set-Mailbox jonny -CustomAttribute1 'Alumni'

As you say that this does not work for you, the solution that is adopted by many people is to establish an on-premises Exchange Server specifically for administering the Online schema. It is said that Microsoft Support will upon demand supply you with a free Exchange serial for an on-premises installation that can be used only for that purpose.

A commercial product that may help is 365 Command Active Directory Extensions. This product adds tabs in AD that you can use to set the needed properties. The custom attributes you mentioned are included in the list handled by DirSync.

What I ended up doing finally (all those months ago) is use the Exchange Setup to only extend the Active Directory Schema. The actual command is setup /ps - this doesn't install exchange but it extends the Active Directory Schema to include the custom attributes (among other exchange attributes).