If everyone went zero waste then nothing would be added to the landfill, and its methane production would taper out to nothing as a result.
From the top charts for image search "landfill gas chart", suggests methane(CH4) vents heavily for 3-5 years, then a long taper.
Consumers do have some power, but they are not the only ones and we should demand an effort from all parts of society there.
On the other hand, I doubt it is plastic waste that produce methane, an organic byproduct. Maybe food wastes are at fault. In which case your enemy is not overpackaging and may actually be your (temporary) ally