Why don't I see my custom ringtone under Default Notification Sounds?

Just like you put those custom audio files into Ringtones directory for the purpose of using them as Ringtone, you need to put your custom files again but in another directory named Notifications (under /sdcard) to have them listed under Default notification ringtone. That would be sufficient.

Note: reboot the device if the Settings app doesn't show those files after moving in into the relevant directory.

Tested successfully on Nexus 6 running Android 6.0.1.

Edit

Alternatively, you can use a third party file manager app. Quite a lot of popular ones responds to the intent action android.intent.action.RINGTONE_PICKER. When you would tap on Default notification ringtone you would be shown a bottom sheet¹ with the option to choose Media Storage or the relevant file manager app. Using your file manager app browse to the location of your custom audio file and select it.

The benefit of the last approach is that you don't have to copy or move the audio file to a particular destination, so you get to save space. Furthermore, once you've selected an audio file using file manager its entry would remain in available tones until you move/delete the file.

¹ _{If you're not shown a bottom sheet then you might be having Media Storage selected as default app to handle that intent or your file manager app doesn't handle that intent. I recommend clearing defaults for Media Storage from Settings app → tap three dots line and select Show system → browse to Media Storage → Open by default → Clear defaults. If that doesn't help, switch to an another file manager app.}