Use separate canvases with different sort orders. For example, put the quest HUD in a canvas with Sort Order = 0 and the dialogue UI in a canvas with Sort Order = 1.
It's easiest to do this if you add one or more UIs to the Dialogue Manager at design time, instead of letting the Dialogue Manager instantiate everything at runtime. Here are some example steps: (just one way to do it)
1. Create a new canvas named Dialogue Canvas as a child of the Dialogue Manager. So your Dialogue Manager will have two canvases: the original Canvas, and your new Dialogue Canvas.
2. Set the Dialogue Canvas's Sort Order to 1.
3. Add/move your dialogue UI to Dialogue Canvas. Make sure it's assigned to the Dialogue Manager's Dialogue UI field.