rice has so little nutrition, if I were you I might try to stick with gluten free oatmeal and potatoes and veggie soups with your fruit meals in the day, basically a Gerson therapy diet, nutrient dense and grain free.
Under eating can cause a week of feeling great followed by weakness and not sleeping, so you might try increasing your calories and see if you sleep well. If you meed to you could add calories by making a drink of sugar and lemon, it's just lacking nutrition so eat everything else nutrient dense.
oatmeal is about the same as rice, just add some sugar to increase the calories. organic carrot juice is calorie dense and very nutritious and cheap in most places.
I think some nutrient dense fats might balance out your calories and help you feel satisfied after a day of carbs. Depending on where you live, avocados might be cheap. If not, you can go for maybe hemp seeds (generally not cheap but great in nutrients), sesame seeds, nuts, or sunflower seeds. Nuts are generally a little pricey and sometimes hard to find raw and unsalted (not an issue if you don't mind cooked and/or salt). It seems to me that sunflower seeds would be easier to get raw and unsalted. Try going to a store where you can buy from the bulk bins to see if that's a better deal for you.
I hope you're feeling a little better in-balance by now!