@c0rnelius I would like to report back with the news of full success:
I have updated cmdline.txt to start with:
console=tty1 console=ttyAMA0,115200 earlycon=pl011,0x107d001000,115200n8
And also added the following to config.txt:
usb_max_current_enable=1
enable_uart=1
dtparam=uart0
dtparam=uart0_console
dtparam=pciex1
dtparam=pciex1_gen=3
dtoverlay=disable-wifi-pi5
dtoverlay=disable-bt-pi5
All this with the HAT+ (in the picture above) still connected.
The early boot console also works, and I also get a login prompt, which is all I wanted.
After this I tried replacing ttyAMA0 to serial0 in cmdline.txt, to see if there is any difference, but they both seemed to work in the end.