First of all, it’s important to have backup strategies, always! While I may not like mixing in my headphones, I can and will when I am faced with a situation where there is no monitor or only a really shitty, useless one.
But even if all that fails (I have had my headphones crashed once by a drunk customer in the days before everyone had earplugs for their phones (I mean to say there was no alternative for my headphones). I ended up drop mixing all night and working the mic more than I usually would. Was it my best night ever? No. But it was acceptable, people enjoyed the evening and went home happy.
There are so many other transitions possible than just beatmatched. Sync is obviously a help, especially with visual feedback by way of parallel waveforms.
I’d just say to the cafe that you didn’t know what came over you that night, that – based on our 6-month history – you are sure this was a one-time occurrence and you’ll make sure it won’t happen again. Lock yourself in your bedroom with your gear and practice the crap out of mixing in your headphones and using alternate transitions.