How can I build a compact EV3 gearbox? I'm building a sumo bot in EV3 and would like to have both 1:1 and 1:3 gear ratios, with the first being useful for general driving and the second more for pushing other robots.

My problem is, I cannot seem to figure out how to get the actual gear switching (moving a + shaped pin left and right on both motors) working. I have only the EV3 parts. Advice greatly appreciated.
I think it's quite limiting to only consider parts in the standard EV3 sets. Many technic sets have gear switches. I believe the cheapest set currently available that has it is the Race cart (42048), the switch can be motorized as was done for example in the motorized excavator (8043). Also the pieces are readily available on bricklink quite cheap.
I think it is a great idea to have a gear switch in a sumo bot, but the only reliable way to do it is use pieces designed for that.