Thanks Michael! I was asking myself exactly these questions when reading the article.

With the French branch of Anima International, we also made similar estimates to evaluate our work with school and university canteens in France. We plan to make a post about this analysis. The results made us decide to look for more effective interventions.

A few points about your post:

• We used a similar methodology as you. In particular, we didn't estimate the number of animals lives saved, but the number of days of suffering averted (as you did). See our recent post: Fighting animal suffering: beyond the number of animals killed
• in France, the breakdown of different types of animal products is different in canteens than in households (relatively less chicken meat is eaten in canteens than in households for instance). It may also be the case in the UK, which would decrease or increase the cost-effectiveness, depending of which types of meat are over-represented in canteens
• even if we advocated mainly for plant-based meals in France, often our partners implemented vegetarian meals, which often contained eggs. Since egg meals (particularly coming from caged hens) cause a lot of suffering (approximately as much as in chicken meals), it signifcantly lowered our effectiveness. So it would be worth checking in your analysis that the meals were shifted to 100% plant-based ones
• all this discussion doesn't take into account the long-term effects of having children eating more plant-based when they are young. We tried to review the scientific litterature about such effects, but we concluded that it hasn't been studied enough to support continuing this program. 

Another good example of the difference between the number of animals killed and the number of animals alive at any point in time is with shrimps and insects. This report (Shrimp: The animals most commonly used and killed for food production, see figures 1 and 2) from Rethink Priorities estimated that in 2020 : 

• the total number of farmed shrimp killed per year is equivalent to 40% of the number of farmed insects slaughtered to produce food and feed and others that die prior to being processed
• the total number of farmed shrimp alive at any moment is equivalent to 2.7 times the number of insects alive at any point in time on farms

(Note that the number of insects farmed may have increased since 2020)
Thanks @William McAuliffe for pointing that out to me.

@saulius Any update on this point ?

Thanks for your reply Bob :)

@Laura Duffy @Bob Fischer 
A question about your methodology : If I understand correctly, your placeholders are probability-of-sentience-adjusted, but your key takeaways are not (since they are "conditional on sentience").
Why having adjusted for sentience in your placeholders but not in your key takeaways ?

Yep, we agree. I meant that the degree of certainty of "an egg meal produces more suffering than one beef meal" is much bigger than your formulation implied. ie : "higher, by some calculations"

I think that my message was poorly written. I'm really not a specialist on this question so I don't know if there exists an egg brand that doesn't produce net suffering. 
I just wanted to say that the beginning of your post ("I'm not a vegan, but I've long felt troubled by the fact that eggs have such a high suffering-to-calorie ratio — higher, by some calculations, than beef") seemed inaccurate. 

I'm french so I have nothing to say directly about your question, but I would like to emphasize that most types of eggs are almost certainly way worse than beef and pig when considering animal suffering.
Using Faunalytics estimates, eating these different dishes creates this quantity of suffering : 
 

• chicken : 0,1 animal live et 5,2 days in farm
• pork : 0,002 animal life and 0,33 days in farm
• beef : 0,0004 animal life and 0,33 days in farm
• egg (omelette) : 0,01 animal life and 4,9 days in farm 

And it doesn't account for the relative badness of being a broiler vs a laying hen vs a pig vs a beef. 

Also, the Welfare Footprint project estimates that cage-free hens live better lifes than caged hens, but still painful lifes.