You can add mixed veggies to your rice, too. If they're fresh/frozen, just saute them with the onion to soften them a bit. Canned just gets added just before The eggs get scrambled. Do you scramble them up right in the pan or add them fully cooked? If you haven't tried frying them in the same pan, I highly recommend it! Just push your rice mixture out to the edges and pour your raw scrambled egg into the center to cook. You can add a dash of soy then too, if you want. As the eggs cook, just stir them quickly into the rice. It's amazing!
We're big rice eaters, here. I keep it ready-to-go in the fridge pretty much all the time ... and you're right about using pre-cooked, cold rice. It gives you a better texture!
Additional thought - a scoop of the finished product and a little bit of chicken, beef or veggies makes a great packed lunch. People always think I ordered take-out!