Have you tried a high end Vitamix? There is a reason they are so expensive. One of which is the high power and special shape that creates a powerful vortex that doesn’t just spin but strongly lifts and folds ingredients vertically. I’ve never had to disassemble or reach under the blade to clean. Just add dish soap and blend to clean.

Another aspect may be the order in which you are adding blending ingredients and whether there is enough moisture to lift and fold. Throw just carrot in a blender and yes it’ll end up trapped under the blade. But first create a slurry of higher moisture ingredients and then add carrot and it’ll work.