You're not factoring in anything from a level 5 orphanage in this scenario. While there may be a lot of players that don't have a level 5 orphanage, there are still a lot of players that do.
For those that had a level 5 orphanage prior to part 2 starting it was possible to have around 10 puddings crafted by the time the cottage was introduced.
So assuming another 40 puddings are needed:
40 X 25 = 1000 of each item needed.
1000 divided by 8 days = 125 needed per day.
Collect cottage 4 times a day = need 32 cottages
Collect cottage 5 times a day = need 25 cottages
But that's still not factoring in a level 5 orphanage. If one could collect from the orphanage 8 times a day plus Ivy one time and old Thomas one time, then 100 per day would be all that is needed from cottages and that could be accomplished with 20 cottages at 5 times a day or 25 cottages at 4 times a day. Then there's the possibility of collecting from the orphanage more than 8 times a day. If someone could collect from the orphanage 16 times a day then one could get by with 15 cottages. I'm not saying that's easy to do but it is possible. And we STILL don't know if anything else will come along to help or not. I just want to present the other scenario so everyone doesn't assume the math is totally impossible.