unpopular opinion in this US-centric forum, but just burn the bags when they end up in the trash. Much of Europe does that. Bags are just hydrocarbons and burning them completely releases nothing but CO2 and water.
Then the landfill ceases to be an issue and we can focus on CO2.
Well, CO2 is a problem, but plastic bags are already more CO2 efficient than any alternative bags given the average number of uses in their lifetime.