OK, it can be done but the solution is non-obvious (I found it in a Microsoft support post).
Go to Settings > Apps > Outlook and click on permissions. Give it "storage" permission, and then it will see the sound files in your /sdcard/Notifications folder. Without that it will only offer the system notification sounds.
The funny thing is that there are other apps that behave this way, but because I'd given them all Storage access I'd never noticed it.
(I actually uninstalled Outlook a while back, because Nine does everything Outlook did for me and more, making Outlook redundant. But I reinstalled it temporarily in order to make sure that this fix did actually work before posting).