It only took me 18 months or so :), but I've published my paper that partially addresses this question, Price-, Taste-, and Convenience-Competitive Plant-Based Meat Would Not Currently Replace Meat.

There is a ton of research tracking the environmental impacts of various crop products. See for example our world in data: https://ourworldindata.org/environmental-impacts-of-food

Tracking the animal welfare effects of crop products is much more difficult and involves thinking about very complex ecosystems. Brian Tomasik  has some work on this as does the Wild Animal Suffering Initiative ( https://was-research.org ). I personally think that where you come down on the relative rankings of various foods will come down to your opinion about the probability and intensity of insect suffering. In my view that probability is quite low but the number of insects is large enough that it is certainly worth considering.

I would classify the next category of harms as "human conflict harms" which would include things like slavery in the production process or frequent violence over production disputes. These harms are very product specific and I have seen a lot of research and discussion about individual products but not a comprehensive list or ranking of various products. It is also worth noting there is a lot of heterogeneity within particular products. For example, chocolate has a problem with child slavery in the supply lines but some brands have done a great job transparently ensuring that no slavery occurs in their supply chains. I do think this is an area that could use a synthesis of the existing research to explain which foods are most problematic in this areas (and where applicable, what brands/countries avoid issues). One thing to keep in mind about this category though is that they are often not inherent in the production of any particular product. It just happens that certain foods are associated with these harms. If we launched a successful campaign to stop eating chocolate, for example, it is not clear to me that child slavers wouldn't just switch to forcing children to grow coffee. Seems like we need a more general approach like supply-chain certification and regulation for a lack of slavery (fair trade certification does this but also unfortunately has some other problems, so I would like to see a certification that is strictly limited to the lack of slavery). 

The author of the paper you mentioned also discussed some harms that are in my opinion non-issues. For example, the fact that global demand for quinoa has priced local growers out of eating quinoa seems like a net-good for them because now they have higher incomes and can afford more of other types of food.

I happen to think that the harms from animal agriculture are orders of magnitude higher than the harms from  plant-based food products on average, but I certainly agree with you that we should not consider transitioning society to veganism as the end-all fix to our food system (though it would certainly be a good start!).