Stale pizza would translate to dog food here... but nobody said decomposition was pretty! Another option for the more squeamish is to slightly bury stuff that is or might turn icky. Dig a little hole next to the roses for example, drop your load, cover it up. Done, no need to move that later, like 'finished' compost. Anything that can go in a final spot the first time, that's what I do with it.
Buried or used as mulch, both forms of sheet composting. I was already arriving at this more lazy conclusion, then a back injury, then the ants convinced me I wouldn't get anything from a pile here anyway. It's all going to go on beds, might as well go there the first time I move it. It will decompose as mulch or in a pile, and seems like the closest thing to a natural plan as I can get, though even if I could still fork up heavy loads of compost and cart it around the yard, I don't think I would. Nobody moves compost around in meadows or forests, it just doesn't make sense to me vs. what I've been doing the past couple years.
The barrel I mentioned above, after dumping icky (green) stuff in there, when I don't feel like digging, or it's a big load of something, I cover it with leaves (brown.) This keeps critters such as flies from being able to access it, as well as provide the balance of materials necessary for the most quick type of decomposition. An odor or slimy conditions are sign of a predominance of greens, anaerobic decomposition. By adding browns, maybe stirring a bit, the balance can be restored so this odiferous process stops. Then a layer of browns on top to block as much access as possible. With a big load of icky, put a little in, then some leaves, then more icky, then more leaves. That mixes things up so the decomposition can begin quickly. Spreading some stinky, slimy stuff on the ground will also stop the anaerobic decomposition by allowing oxygen to react with most of the surface area. There's nothing wrong with smelly, anaerobic decomposition, except that it's offensive to the olfactory senses, so efforts to avoid that are worth doing, and not hard to do.