KitchenAids are great but even well adjusted there's a limit to how little you can put in. It partly depends on the ingredient. For instance, creaming small amounts of butter and sugar can work if you scrape the bottom often with a rubber spatula. Once it gets going and starts to cream it usually is fine. Cream and egg whites are similar. Batters are a different story, you can end up doing as much manual mixing as machine mixing.
I wouldn't recommend spending money on a smaller bowl as it's unlikely to solve the issue, which is clearance between the attachment and the bowl. For small amounts of ingredients my tool of choice is a stick blender with a whisk attachment, it's a lot less mess and much more effective because you can get it into contact with your bowl and get all the ingredients in the mix. They are pretty cheap, you should be able to find something for less than $60.