I did similar calculations and thought the same thing - I also run a 38" tire. However, I didn't account for the fact that a 38" tire weighs so much more than a stock 31" tire. So while the engine RPMs calculate out to the same, it simply isn't the same scenario due to the tire weighing so much more.
The graph below indicates that yellow is for increased fuel economy, black is for stock-power feel, blue is for improved power. You're kind of on the line between fuel economy and stock power. However, this chart still doesn't take into account the weight of an oversized tire and looks more specifically at engine rpm. I doubt those yellow blocks are actually accurate as indicating improved fuel economy when the tire size is increased.
If you have the opportunity, I'd say a 4.88 gear would be good for you. That would give you acceptable power, reasonable fuel economy, and protect that new transmission you've got.
"alexsdad" has 4.56 gears and 37" tires and he says his truck is gutless. He only drives his to the trail, so it'll probably hold the transmission fine for a good long time. However, since you do mostly city driving, meaning more stops and goes, I think you'd be better off to go a little deeper on the gears. I really would be surprised if your fuel economy is hurt by getting more appropriately sized gears for your tires.
Not intending to sound preachy - I'm relatively new at this stuff. Just would hate to see you end up with a shot transmission.
Finally, I'm getting my TBI truck squared away this week with the lift/tires/etc., and I'll be running 5.13 gears. Once I check the mileage, I'll report back and you can compare. What are you getting out of it now?
Where did you get them from?
