The first option (Detailed analysis of the nutrients from typical kitchen waste), primarily reveals the nutrients that were not properly utilized and have gone into kitchen waste. You would need to find out that how these nutrients would contribute in enhancing soil health when that become part of compost pile. You would have to make sure that nutrients generate some beneficial properties for soil while they are composted and do not generate any harmful byproduct for soil.
The second option (Information on how to construct a productive compositor system) would provide a generalized analysis instead of primary focus on kitchen waste.
The third option (Personal testimony from a family who composts 90 percent of their waste) is likely to provide a guided tour but that would be specific for that family and soil around their property. If that property is in a specialized climate (such as desert in Arizona or wetlands in Oregon) then those factors would need re-calibration for the climate and soil that you would propose.
The fourth option (Studies indicating an increase in home production of vegetables) might provide you region-specific soil information as well as generalized waste information for different areas/communities.
In my mind, the last one could be more relevant one with relatively less time-consumption for research and more precise information for recycling the waste in the best possible manner for the environment and community health.
Hope this is clear and helpful to some extent.
The second option