You're not the first person to run into this, the power LED's combination of current and low voltage is tough. Linear regs and resistors are not really practical.
The key is a simple buck converter in constant current mode. This not only means no heat is generated but you get more current out than drawn from the supply. In your case a 12v 200mA supply would do fine.
The easiest (and cheapest) thing is a Supertex LED driver. You need one of these, a MOSFET switch, a small but properly chosen inductor, a low ohm shunt resistor, a Schottky diode, and a few typical resistors/caps.
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You mention 1W devices but talk about driving 2.24W to them. Is this for 2 or 3 or what?
What device do you have? The thing to be careful of is these devices can generate a good deal of heat. A bare emitter will destroy itself almost immediately if not heatsinked. Even a 1W Luxeon Star needs to have consideration given to its mounting to make sure it doesn't overheat.