First, your calculation is correct. You could use a 560, 620, or 680 Ohm resistor (standard resistor values). However, there is likely no need to run the LED at full current. For just indoor panel indicator use, I typically use only 5 or 10mA, which gets you closer to a 1K resistor.
For some battery powered applications where the LED current is a significant fraction of the total power, I have used some "ultra-bright" LEDs, and operated them at ~1mA, and they are still good to go, even when viewed outdoors in sunlight.