You can use the display and Hats. I screwed the display driver board to the display and then added the Pi and then three other boards stacked on top of it. The only tricky part is getting power for the display. it wants 5V and the pins available for that in the GPIO header are occupied with your hat. There may be a place on that hat to sneak some of the system 5V out. I soldered to the GPIO header pins under the Pi to steal the 5V (the yellow and black twisted pair in this pic). Here’s a pic:
There are a few plastic case which look “okay” and don’t enclose the Pi at the back, so the HATs can simply be stacked into the air as required. As to power, one can use a split USB cable to power both the display and the PI — it isn’t required to use the pins. EDIT: sometimes with an additional HAT you may not have enough power, even with a 3A supply, so you will need to adjust. I was too cavalier in my original words.
I also use a few “display-only” configurations, so I can place the display where it looks best and place the audio end-point where it close to the DAC.