Fungi are kind of bottom-feeders. Currently, mushrooms are low in carbohydrates, low in fats, and low in protein (except in a Dr. Who episode I watched once). The fungi would need to be breaking down high-calorie materials (not generic wastes) in order to have enough energy to make all these things, even with genetic engineering. They are high in certain vitamins and minerals (see the list). Lots of things like to digest high-calorie foods, so your super-fungus has a lot of competition. You could easily expand it's deposition and collection of additional minerals from whatever foodstuffs they are consuming, and increase the number of vitamins the mushrooms synthesize.
While there isn't anything that you couldn't insert genetically into a mushroom that would stop it from having these properties, it's hard to compete with a plant, which can input free energy (sunlight) into the manufacturing of all this stuff. In the case where you have high-calorie inputs (like, say wood pulp or recycled paper/plastics) there could be some fascinating applications - imagine this as a landfill digestor. Then focus on ONE aspect of your fungus idea, and make the mushroom lavish it's efforts on part of the food chain (like giving it genes to make balanced proteins).
I would likely focus on the fungus as a liberator of carbon and nutrients from otherwise hard to digest materials, and funnel those nutrients to plants and algae that have been engineered to do all those things. After all, why reinvent the apple, when your fungus can make the fertilizer?