iTunes still looking for local file instead of the cloud

I have finally completed the process of matching and uploading my library with iTunes Match. My original, local library is located on an external HD, connected to my MacBook. Now that everything has uploaded, I quit iTunes, disconnected my local drive, then restarted iTunes. But every song now has the exclamation point symbol, and when I click it, I get the "cannot locate the original file" error message. All the while, the iCloud status for the songs is "matched". Why doesn't iTunes simply play from the match? (Yes, I am connected - via cat6 cable - to the internet.)

If I click "Cancel" on the "locate file" error message, the file will pull from iCloud and stream it (as well as give the symbol that it is available for download). But just that one file. If I am in a playlist, iTunes won't proceed to play the next song, it just stops. So I have to click each song on the list manually and click the "cancel" button manually for each. Then they will play from the cloud repeatedly, so long as I don't log out of/shut down iTunes.

My questions is: is there a way to get iTunes to look to the cloud first? Or is this MacBook forever a "home base" that must remain connected to the actual files via the external HD, and the only solution is the aforementioned tedious manual clicking each file to force iTunes to look to the clouud?

(And yes, I did turn off iTunes Match and log out of the iTunes store, shut down iTunes, then went back in and logged back in to everything before I wrote this.)