Most of these analytics providers also allow you send data from your server that you can then correlate with your visit data. While I think solutions like this works initially, in my experience you will spend a lot more time building the capabilities that an analytics package could provide out of the box with little work. For eg., being able to visualize tracking live as it happens is something I have really gotten used to.

I'm not familiar with the other analytics providers, but can't you track certain events (like orders and charges) and bind properties to them using Mixpanel? This could help you reconcile the data in your database.

you can track server side events with google analytics too (if using universal analytics).

I would have no idea how to add the data if you hadn't been tracking it already though.