If the dAISy input solution does not work you will not be able to use UART0 because it is being used by the HAT but I can see that you have a Raspberry 4 so you can also use UART2, UART3, UART4 or UART5 soldering TX from the module to the right RX GPIO in the HAT. You have to be careful with soldering but it will work for sure.
Let us know what Adrian says please.
Let us know what Adrian says please.