Apologies for the inconvenience! While it's not possible to control the layering with sprites created in other plugins, one solution could be to have certain HUD elements become completely hidden while dialog is occurring.
If you use a "Custom Code" display condition, and input the following: "return !$gameMessage.isBusy();" the component will only appear when there isn't a "Show Message" type event active.
If you're using the "Pro" version, you can even have them fade when appearing/disappearing by using this animation: "Property => Opacity", "Start Opacity => 0.0%", "End Opacity => 100.0%", "Duration => 8", "Activation Type => On Show/Hide".