Sounds like a typical switch matrix issue with a shorted switch capacitor or diode that's ghosting an outhole trough switch.
Switch test mode is you friend.

Raise all the drop targets and remove all three balls from the outhole area.
Open the manual to the switch identification page (printed page 17, electronic PDF page 21).
Get the game into switch test mode.
Activate each switch in reverse order from number 40 down to number 01 (as assigned in the switch identification chart in the manual).
When activating drop targets, leave them down. Activate trough/saucer switches and leave them closed. Make sure the actual outhole switch (01) is activated last (don't put a ball there to hold the trough switches because you won't be able to sense them).

Take note of any switch closures that report the wrong number.
You must activate switches in reverse order because switch test mode will only report the lowest number switch that's closed.
Keep your hands off the side rails (ground) so you don't get any phantom activations across the matrix.

Did any switch(es) report the wrong number during the process?

To re-iterate the process. Start at switch 40 (left pop bumper). Press the pop bumper skirt and 40 should appear on the displays indicating that switch. Release the switch and do the same for switch 39 (right pop bumper). When you get to switch 35, drop the drop target and leave it down (game should report 35). Move through next drop targets in order and leave them down after activating them. When you get to the saucers, leave a ball in them so they stay activated.
When you get to the outhole switches you need to do them in order and leave them closed (like a ball is closing it).
At the end you should be left with 01 showing on the displays since that's the outhole switch that the ball sits on.

The idea is that for momentary switches you just press them momentarily to see if the game senses them. For switches that can be continuously closed (drop targets, saucers and outhole/trough switches), they need to be held closed after you activate them and move to the next lower numbered switch.

The key thing is whether any (and which) switches report the wrong number.

Check your coin switch wiring. If you have a stuck or shorted coin switch you can have matrix issues like this.

Not that it matters much but those two cut red-green wires (where there's no centre coin switch) are supposed to be connected together for the coin chute switch closer to the lock to function since the red-green wire is daisy chained to each coin switch.

If all switches report correctly in switch test mode as per the processes I mentioned above then you might have a phantom switch activation issue caused by high current noise.

Do you notice if the phantom outhole switch activation is happening when the doodle bug mech is putting on its show, or maybe when you press a flipper button particularly the right flipper?

The description of the issue is not the game resetting. It's the game incorrectly sensing the outhole switch activating; counting down the bonus, resetting the drop targets and moving to the next ball number *mid ball*.

@timab2000, I know you said it's random but roughly how often does it happen?

Next time it happens, (you notice the bonus countdown happening) immediately switch the game off. Take note (photo) of all drop targets that are down and whether any balls are locked in the saucers.

One thing I suggest trying: the MPU J2 connector has two wires running to another in loom connector in the head (white-green wire and grey-yellow wire). Please disconnect that two wire connector - it's for the post kicker button switch next to the right flipper button in the cabinet. The wiring to that kicker switch picks up a lot of electrical noise from the flipper wiring and one of those post kicker switch wires is associated with the outhole in the switch matrix which is where you appear to be getting phantom activations.

The siren is a slam tilt indication. Look at all the tilts - the ball roll cage on the cabinet is usually suspect here.

There's one on the coin door, and possibly one on the playfield underside.

Did the slam tilt happen to occur when the doodle bug bouncing ball was active?

Probably time to just replace all the switch capacitors (if you haven't already).

The capacitor you've got wired on the tilt plumb bob is connected to the wrong location. It should NOT be connected across to the slam tilt switch, rather that end should be connected to the lug screwed to the tilt board with the two blue-orange wires.
i.e. one end of the capacitor connects to the white-black wire at the outer plumb bob brass ring (as you have it), the other end of the capacitor connects to the two blue-orange wires just above it. That's why those two wires are soldered to that lug.

There's no need to investigate the ground issue in your video any further. Every Bally will do that. You grounding the switch return lines is injecting noise into the system that it's picking up as phantom switch activations.