Welcome aboard!

Looks like your mileage didn't change, much. Your dealer didn't (and can't) reprogram/correct the speedo/odo. The changes they make in the PCM ONLY correct for ABS operation. The tire change increased your roll-out by about 5%, which corrects your fuel mileage almost back to where it was before, but not quite. While taller tires offer a potential for an economy improvement, wider tread reduces it (for a number of reasons). Switching to a 235/85/16(32") or 255/85/16(33") offer the best opportunity for an increase.

Power programmers won't improve your mileage, generally. They may offer the opportunity to help you improve it, but ultimately, it will be your driving style and habits that will determine the actual outcome. The Predator programmer (Diablosport) will allow you to correct the speedo/odo for tire size changes and increase power, but won't help fuel mileage by itself. Only your right foot will do that. Normally, having more power on tap temps one to use it, which will in every case, decreases mileage. The advantage of having more power allows you to drive under the same conditions in a higher gear (under load or ascending a grade), which can increase economy, provided you resist the temptation to use the additional power. If you get/use any power programmer, be sure to also install, at the very least, an EGT (Exhaust Gas Temp) gage. A boost gage is also recommended, but the EGT gage is necessary to monitor the exhaust temp, which can cause sever engine damage if exceeded, or prolonged.