Most of the LEDs I use; the current X voltage get close to 3W.
Remember 3W is with a heatsink!
The white LEDs in a 3W case also come in red, green, blue, IR, etc. with different forward voltages.
My thought is that the case is "3W" and the higher voltage (white) LEDs are 3W. To make designing easy the IR version typically has the same package, the same current but different Vf and thus different wattage.
I have made flashlights what sold in several different colors and we only changed the LED, not the current regulator. (note I did not say voltage regulator)
how much does the peak and dominant wavelenght of an LED shift when the forward current changes from say the 350mA used to calculate the wavelength and the 700mA absolute maximum forward current?
That depends on the type of LED. A red LED will change very little over 2:1 current change. (any single color LED)
White LEDs are made in several different ways. I am using white LEDs that have phosphor over the silicon. (the LED excites the phosphor, much like a CRT monitor or florescent bulb). In this case the color of the phosphor changes (some) with current.