What's the best way to recover carts with out-of-stock items?

I'm losing my mind with out-of-stock situations. Every time a customer adds a product to their cart and discovers it's unavailable, I feel like I'm watching potential revenue just evaporate. My team and I have tried manual email follow-ups, but they're time-consuming and often feel impersonal. We're a growing fashion accessories brand, and inventory fluctuations are killing our conversion rates. Sometimes products sell out within hours, leaving customers frustrated and our sales funnel completely broken. I know customers don't want generic 'sorry, out of stock' messages—they want solutions, alternatives, and a seamless experience. Our current approach is basically crossing our fingers and hoping they'll come back, which is about as strategic as throwing darts blindfolded. We need a systematic way to keep customers engaged, offer meaningful alternatives, and preserve the momentum we've built through our marketing efforts. This isn't just about recovering a single sale; it's about maintaining customer trust and preventing long-term revenue leakage.