I think what the OP wants is to set a velocity curve on the analog signal, similar to a graphic tablet pen's pressure curve. This is not something that can be done from Dolphin, it only allows for setting a dead zone and a valid range (via calibration) unfortunately. If you are lucky enough to have the driver/software for your controller that lets you set this in some other control panel, you could set it there. This is a growing problem with newer analog controllers as they have finer resolutions, which is great but not so great at the same time. When using it with older games, they will not expect you to have such a fine resolution in the first place. In newer games they work great because newer games expect such a controller.
Dead zoning will not work here because we are trying to decrease the output as the input value goes down, dead zoning just cuts it off -- not what you want. Calibration really only helps if you are using the older controllers that didn't filter and correct their own analog inputs, you will find most controllers do this themselves (unless it's just a really bottom-shelf brand, which even that I've not seen in some years).
Dead zoning will not work here because we are trying to decrease the output as the input value goes down, dead zoning just cuts it off -- not what you want. Calibration really only helps if you are using the older controllers that didn't filter and correct their own analog inputs, you will find most controllers do this themselves (unless it's just a really bottom-shelf brand, which even that I've not seen in some years).