If you have a slow cooker as Catija suggested, you can totally do exactly what you want. Search for slow cooker rice pilaf if you need a starting point. I know you don't want new appliances, but slow cookers are a bit more general purpose, so maybe you have one or would be okay buying one, and future readers certainly might.
I'm also pretty sure the oven will work, but it might require a little experimentation to get the timing right. There are again a lot of recipes for rice pilaf in the oven, but they normally start with boiling water then take perhaps 45-60 minutes for white rice or 60-75 minutes for brown rice, at 350-375F, so they'd be very overdone after three hours. But if you reduce the temperature, you can extend the cooking time and make it more tolerant of cooking past done. A slow cooker isn't really very different from a tightly covered dish in an oven at a low temperature.
So, if I had to hazard a guess, I'd take a normal oven rice recipe (with the water boiling before starting), and reduce the temperature to 250F, then see how long it takes to be done and whether it's okay after three hours. It'd really be best to do a trial run sometime when you can actually check on it, though.
If that doesn't extend the time enough, you can probably stretch it even more by starting from non-boiling water, but I unfortunately don't have a good sense of what combination of water and oven temperature would accomplish a three-hour cooking time.
If you don't want to experiment, your fallback of reheating can work too. The key in my experience is to add a bit of water then cover when reheating, so that it steams and moistens again, rather than getting dry and hard.
For one to two servings I just drizzle a little water in, maybe a couple teaspoons, before popping in the microwave. For a larger quantity like your situation, probably a bit more than that - the idea is that it mostly but not entirely boils away by the time it's all reheated, so that the rice isn't wet, but has been surrounded by steam the whole time. You can always check on it in the middle and see if it's nice and steamy, and add a bit more if it's starting to seem dry.