Water is coming out of the sewer cleanout. So I'm assuming that's where the waters coming from puddled in my front yard.

But when I shutoff the water to the toilets, and turn on the water at the main, there's still water coming out of the sewer cleanout, and my water meter is still reading that water is going into the house somewhere. Thoughts?

Is your toilet running? If not why shut it off? A toilet is always shut off until you flush it unless the flapper leaks. Now this turning on the main, when you do that if the water meter is running and no water running in the house faucets or anything on, you must have a broken water line past the water meter. As far as in the house water pipes and sewer pipes are obviously are separate. BUT if that water line brake was beside a sewer line that also had a break then this could cause your loop problem. I've never seen this before was it cold and your waterline froze and possible the sewer line has a crack competing that loop.

What you should be concerned with is the stoppage from the cleanout to the curb .