How are you guys handling 24/7 support without losing your minds (or outsourcing to a BPO)?

I'm running a small Sa⁤aS with customers in the US, Europe, and Asia. Right now, our "24/7 support" is basically me waking up at 3 AM to check emails or customers getting a "We'll be back in 8 hours" auto-reply that does nothing to help them. I really don't want to outsource to a cheap call center, our product is too technical and I care too much about the br⁤and voice. But the "Monday Morning Backlog" from the weekend is killing my team's productivity. Has anyone successfully used AI to actually solve issues after hours, rather than just saying "we received your message"? What's the setup look like?