It depends what you want to achieve.
If you're driving for economy then shifting at 3k or below will do.
Our cars don't make much torque at low RPMs so you really have to be higher up in the rev range to get going.
In your GTS 'lift' should start kicking in around 6.2k RPM (your engine also has to have reached the proper operating temp), this is where you'll start making peak horsepower. The cam profile changes and your Intake
/exhaust valves will open more and for longer allowing the engine to breathe better and you get more power.
Basically, driving for economy - 2.5-3krpm, spirited driving then maybe near redline :P.
Don't rev the tits off of the car until it's reached operating temperature and perform regular oil changes and then you can change gears when you want. For instance, I will shift around 3k when I first start the car and once engine temps are good I will then start shifting higher if I want to accelerate faster.
Lower rpms = less power - if you shift too low you will get barely any power, especially going up hill.
Our cars are high-revving low torque engines so I think what you're describing is just the nature of the beast.
With regards to rowing through many gears quickly - it's also the nature of the car. I often skip gears, for example I will get up to speed in 2nd gear and then shift to 4th, (missing third), and then go to 5 or 6 depending on my speed.