The simplest approach is an eleven pole, three way switch.
You can make one using three of these wafers:
On a suitable body mechanism:
That gives you a switch with twelve separate three-way sections; use ten for the signal contacts and another to switch the LEDs.
Each switch section has a common (the output at the right in your diagram), the contact that always connects to the centre disc in the wafer, and one contact for each switch position, connected by the tab at the edge of the disc as the switch is turned.
Use the first and third position contacts for the A and B inputs. The centre (position 2) has everything disconnected.
Another switch section would have eg. a 9V battery + connected to the common, and positions 1 and 3 to each to a 470 Ohm resistor and a LED for the indicators. The negative/cathode side of the LEDs goes back to the battery negative.
Or use a four cell AA battery holder and 220 ohm resistors, as you prefer.