From those specifications, it is not obvious that these drivers are actually constant current (CC) drivers. Let's suppose, they are. Then you can drive your LEDs with them directly. If you want dimming as well, you can probably do that only if these CC drivers have PWM control input. Normally, you cannot put a PWM dimming circuit after a CC driver, you have to implement dimming within (with the help of) the driver. That's because an average CC driver might not tolerate fast switching of the load on/off. If the documentation of the CC driver states its ability to cope with a PWM-switched load, then it's fine, otherwise probably not.
To drive LEDS, you have two options, each with their own pros and cons
a) linear
b) switching
a) linear, dissipates excess heat, simple (LM317) (or relatively simple)
b) switching, low dissipation, potential switching noise
To choose between these two, and then to choose which way to implement either, you need to look at your other constraints. Heat? Cost? Board area? Able to control finely? Design skills?
You can get integrated solutions for both methods. Maxim IC do a gazzillion drivers in both types, try sampling them for one or two.
Linear devices will always get hot. At 0.5A, with a few volts drop, you will always need to think about heatsinking, whether you use an integrated or discrete solution
FWIW, my personal preference for a linear multi-colour driver, and OK, it takes large board area, is a discrete solution. Each channel uses a TO-220 MOSFET, with a small resistor in the source to monitor sink current, driven by 1/4 of an LM324 op-amp, driving the gate to servo the source voltage to maintain the drain sink current, 3 channels uses 3 FETs and 3/4 of the LM324. The compare voltage to the 324 inputs allows you to set the currents. The heat dissiaption is spread over several big cheap devices. TO220s are good for 1 to 2 watts in free air, to 100watts on a heat sink, so it's scalable to many amps and higher voltages, still staying with cheap MOSFETs.
There are so many integrated LDO (low dropout) regulators available that can be configured as current sources that it would be futile for anybody other than you to start trawling through them. Look for voltage input range, heat dissipation, package size, AND ABILITY TO WORK WITH WHAT TECHNOLOGY STABILISATION CAPACITOR, ie ESR (ceramic, tant, alli elec), as you don't what them to oscillate in service.
To do without the heat, investigate integrated switching solutions.
Best Answer
You have not mentioned the color of the LEDs. The typical white LEDs that make up modules like yours would take more than 3V to reach maximum rated power. I would say around 3.5V could be a common number.
For a 3.5V white LED, probably around 20% of the voltage drop is due to ESR. A LED (of the same base color) requiring lower voltage and therefore has a corresponding lower ESR would be more efficient.
So there is an unavoidable resistor in series with every LEDs already. If you use the number 12V, 0.6A, 20% ESR then the ESR = 12 * 20% / 0.6A = 4 ohms. These are guesses and may not reflect what you have. But say if these guesses are exactly right, then you would get 1A at 13.6V.
(The simple ESR model breaks down badly at low current).
Rereading what I wrote, I was assuming 4 x 3V. But there are only 3 LEDs in series, so the numbers do not add up.