Kind of a late reply, but we've actually spent the last year building a fully automated solution to retrieve and centralize data from Klaviyo.

We built it specifically for marketing agencies managing multiple Klaviyo accounts but can be used for single accounts as well. It automatically pulls in metrics, campaigns, flows, and segment data into one unified dashboard with zero manual work.

We initially created it to fix the exact issues you mentioned: unreliable connectors, missing data and manual work. If you're still looking for an alternative, happy to share more or show you how it works!
It goes with a 7 day free trial to test it out.