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.
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.