Erm not too sure tbh, I would try for a CN then if she refuses do EBT. She was obviously shattered though!!
For future, would you consider doing a quick 10-15mins CN at say 9.15am if you think she won't make it to her usual nap time? This is what I used to do with DD when we were further down the transition. Then it could see her through until close to her usual nap time or a little later. Say 12pm. Wdyt? It just helped me with the consistency but it's totally up to you.
When we started the transition I could never do short am/long pm, but what I said above did help us here and there when we were mostly on one nap.