I've got the boards, I have them assembled, all I am still waiting for are the switches, which are already in customs. With the board assembled, I have the joystick working, so I can as well write the code for that.

For now, just for testing, I wrote this short program just to see how well it would work:

import board
import analogio
import digitalio
import usb_hid

mx = analogio.AnalogIn(board.A6)
my = analogio.AnalogIn(board.A2)
lmb = digitalio.DigitalInOut(board.A1)
lmb.switch_to_input(pull = digitalio.Pull.UP)
rmb = digitalio.DigitalInOut(board.A5)
rmb.switch_to_input(pull = digitalio.Pull.UP)

for device in usb_hid.devices:
    if device.usage == 0x02 and device.usage_page == 0x01:
        break
else:
    raise RuntimeError("no HID mouse device")

report = bytearray(4)
last_empty = False
while True:
    x = mx.value - 0x7fff + 2500
    y = 0x7fff - my.value - 500
    report[0] = ((not lmb.value) << 0) | ((not rmb.value) << 1)
    if abs(x) + abs(y) > 4500:
        report[1] = min(max(-127, x >> 11), 127) & 0xff
        report[2] = min(max(-127, y >> 11), 127) & 0xff
    else:
        report[2] = 0
        report[1] = 0
    if report[0] or report[1] or report[2]:
        last_empty = False
        device.send_report(report)
    elif not last_empty:
        last_empty = True
        device.send_report(report)

It's very simple, almost self-explanatory. The only thing that complicates it is the addition of a "dead zone" — an area around the center where the mouse doesn't move at all. Without it the cursor would be always slowly drifting one way or another, which would be pretty annoying.

Unfortunately, the way I implemented the dead zone here is not very good, because it forces you to move the mouse cursor with a certain minimal speed — below that speed the cursor won't move at all. A better solution would be to count the speed starting from the edge of the dead zone, but that is more math than I am ready for at the moment, as it would involve proportions. The horror.

 In any case, it seems to be working reasonably well, despite flooding USB with mouse events. I might also need to deal with that at some point — there is a lot of opportunity for tweaks here, including fancy stuff like logarithmic sensitivity.