I apologize for just skimming here, so I may be repeating stuff...
First, I'd ditch "Eco" mode completely... I've read too many posts like this one where it was eventually determined that fuel economy was better using "Normal" mode instead of Eco...not to mention other threads from folks who compared both modes and had similar findings, particularly for local/city driving. I know it's counter-intuitive to think that Eco mode is worse on MPGs than Normal mode, but my assumption is that drivers are over-compensating for the throttled accelerator response and that Eco mode is just not tuned properly in this vehicle.
You're already driving an expensive vehicle with decent performance, why neuter it with Eco mode when it's not saving you anything? That's just my take...
Second, yeah, those big, heavy off-road tires aren't doing you any favors...12 MPG is worse than I'd expect, but still
Third, my fuel economy did improve a bit after the "break-in" period, but it wasn't anything drastic, i.e. I wouldn't expect yours to suddenly go from 12 MPG to 21 MPG, mine improved maybe 1 or 2 MPGs per trip, on average.
And lastly, on mine (21,000 miles), I've found that highway fuel economy on longer trips has been pretty spot on compared to whats advertised, generally in the low to mid 20s in MPGs...but on shorter trips around town, my MPGs are much more all over the place, reporting anywhere from 15 to 20 MPG when I check after shutting off the vehicle. Distance, speed, time spend idling at red lights and other stops, frequency of having to stop, uphill vs downhill, etc, will play into just how much fuel you're consuming. If you haven't yet, you may want to make a point to take a trip on the highway of at least 20 miles or so, and see what's it's reporting for that...it may give you a better idea just how far off the estimated fuel economy you are and how concerned you should be.
EDIT: For what it's worth, I'm running KO3s on 18" rims (265 70R18, I believe) -- so not the stock tires, but not as heavy or beefy as OP's, I believe.