I've removed hundreds of wads using number 6 from snooker club/pub carpets, and these wads were down for up to 15 years!!
Mind you my arm ached like hell with all that brushing, As I done this pre cleaning there is no issue with residue resoiling, If your not cleaning simply mist eco spotter to the area where the gum was and give it a quick buff with a terry towel.
If lactic acid was not an issue I would get from wad to wad in about 30 seconds which I doubt any other method would come close too.
Paul