Installing a smart thermometer (ecobee4) can I move the wires around on the HVAC?
Go ahead

You can take the blue wire from G and move it over to C on the furnace -- there is room for two wires on the typical furnace-board terminal.  The skinny red and white cable carries the Y and C wires to the compressor contactor on your AC's outdoor unit, by the way, and simply stays put when you do this.