The tricky thing is that these insights wind up being kind of obvious from the first analysis. You will find things like "users who use the software more are more likely convert." Other times these types of analysis will confirm what you already know. The tricky thing is making sure you have the right tagging/events and place to make sure you're getting at the right level of detail to get something worthwhile. It's very a much a garbage in garbage out type of thing.
but we discovered looking for patterns in quantiative data was a waste of time. Instead what we are focusing on is more qualitative data: interviewing customers, interviewing people who cancelled, and finding the "jobs to be done" of your prospective customers. then mapping that to your product features.
once you truly understand your customer needs, knowing what to fix/improve is rather trivial.
Anyway, I'm not sure you'll find what you want with data. Usually you understand what the magic moment is by putting yourself in the position of your customers and then using your own product. Or trying to use your product and identifying the moment where your reaction goes from "meh, who cares" to "oh, wait, this is really exciting!". If you're not your target user, watch your users using your product and carefully observe their facial expressions. The magic moment is entirely emotional; that's what makes it magical.
From my perspective it spreads my risk and from their perspective it means they get access to higher-end analytical help in a more flexible package that meets their needs. Their trade-off is higher rates per hour and my trade-off is a little more variance in income.
You probably heard the story on how facebook realized that once someone adds at least 7 friends, then they reach this "Aha moment", and from that point on, they're converted to longer-term users. And how afterwards Facebook optimized their onboarding experience to help new users find and add more friends...
That's the problem I'm facing with our startup. We have tons of data. We track events, conversions, page views, bounces, you name it. But we're still not sure what's our "Aha moment". A tool or service that would ingest our analytics (or do its own) and find a strong causal relationship between actions and conversions would be really amazing (ideally, without requiring a $gazilion+ enterprise license)