Instead of an aquarium, what about a good sized shallow tub with assorted southeast Asian bog plants? Any rice you'll be able to get a hold of is likely to be bred for yield and not a terribly good houseplant.
I would be tempted to try the northern US wild rices (sure enough, XT87 has that MN tag--home of the best wild rice) but...10 gallons might not work out. And of course if you're going for authenticity, neartic plants won't be the right choice.
My betta lived in a potted plant in an indoor pond and he was the happiest betta. He had about 2-5 inches of water to the soil (depending on evaporation). He didn't spend all his time over the pot--I'm not that cruel. He swam over the entire 6'x2' oval of the pond, but the plant was HIS spot. Yeah, he died, but I'd had him for around 5 years which isn't bad for a petsmart betta.
ANYWAY, I had a point somewhere. O yeah. If the plants are potted, you can make "seasonal" adjustments to the water level, or simply raise the plants above the water level, without making mud. But again, not so well in 10 gallons.
I think you need to do this project, though! Try the tub method. I think you need more surface area than a 10 gallon tank for a proper rice paddy/bog and depth is less important.