Longer average trips and a little thought raises MPG. Short average trips lowers MPG, especially in cold weather. For me with the less than 10 miles a week on slow(25 MPH or lower) local roads in traffic, of course it is lower than others who drive more. I am using a full tank of gas once a month. The apartment hunting trip was a one time event. I filled up in the morning (from no bars on gas gauge). I left then drove 2.5 hours (80 miles) one way to where I was apartment hunting looked at a bunch of apartments and then headed home. Part of the trip was highway, but most was 2 lane paved back roads with some traffic lights, low speed limits and traffic. I still have a 1/4 of a tank left and have driven over 400 miles. Not sure what MPG will be by the time I fill it up and do not plan on no bars on gas gauge again.
I run 34 PSI most of the year on the Pirelli P7s I have on the car. I might report back after I move and go back into a daily commute mode. I don't know what the traffic conditions are in my new home city. It is a place I have never lived or worked. I also do not know how long the commute will be. Best I have ever gotten is 50-55 (IIRC but I would have to check the log book and hand calculate) MPG on the long relocation trips.
I do not speed, I am gentle on my car and the max speed over the speed limit I will drive is 9 MPH but usually stay at the speed limit or 5 MPH over and use the brakes as little as possible and gently get the car to speed. Car seems to like 3000 RPM or less.
With some thought and concentration, I could probably do better, but I like driving and let the car do what it does. Considering the current use of my car except for this one trip, 37 is pretty good IMO.
I personally would not want the tires any firmer.
For the first year from new, I left it in Econ. I think using the modes the way I do now, I get better MPG. Using the car more and for longer average trips, I presume MPG will go up.
I really for me see no reason to beat on the car or push for higher MPG. It does a hell of a lot better than the car it replaced which, if I was lucky, got 25 MPG, and it took 91 octane minimum. That car was a tank of fuel a week or more, commuting a longer distance, and it had an 18 gallon tank. As you said, the CR-Z is doing what it was designed to do without even trying.
OW20 full synthetic here changed by minder or once a year. Air filter, changed once a year. Tire pressure checked every 2 weeks cold in the morning before car moved and adjusted to 34.
But I should not justify any of this to anyone. I am happy with the car and may experiment to see if I can change my habits.