I just wanted to follow up with a little cold water...
I did a rough calculation that at 100% thermal efficiency and 100% volumetric efficiency and perfect air/fuel stoich ratio and perfect 100% burn a 4.0L 4 stroke engine could produce around 1300hp at 4,000rpms. 1,650hp at 5000rpms. 4,400rpms is likely very close to the peak volumetric efficiency of the 1GR. (peak tq = peak efficiency typically). Assuming still unrealistically generous, but more realistic 80% volumetric efficiency at 5000rpms and 25% thermal efficiency, the best any tuner could hope to squeeze out of the 1GR is about 325hp. Possibly a peak of around 350hp at 5500rpms before efficiency really crashes. That's ignoring all of the physical limitations of this particular engine that will make those numbers hard to reach.
So... the point is that a tune is never going to provide significant improvements in driveability at midrange rpms. At very best it'll improve power by 10%, but even that is pretty unlikely. NA gasoline engines are pretty close to the limits of efficiency already. The only realistic ways to get more power is to increase RPMs (pointless in this case IMO), or increase volumetric efficiency (impossible with tuning), increase thermal efficiency (probably impossible without leaning afr), or add forced induction. So... think very hard about whether you wish to spend your money on a tune unless there's a very good demonstration of added power without leaning out the air/fuel mix (engine life) or increasing rpms to increase the hp on paper that we'll never use.