My friends have a fat cranky cat with the same problem. Even though she'd run around and play, she had this huge belly she had to haul around. After switching her (slowly) to a grain-free diet, her energy level ramped up, she dropped quite a bit of weight, and she plays TONS more and is far less cranky. Her coat is much improved too. Cats aren't designed to eat grain, even less than dogs are. It makes sense that feed that's loaded with grain as a filler would cause inflammation of the digestive system and overall make the cat feel crummy.
Some other things you can try is to put her food dish up high so she has to jump to get to it, and/or get one of those slow feeder balls that dumps out a piece of kibble randomly, but the cat has to swat it around to get it out. It feeds into their instinct to bat at something before eating it.