Quote:- "...so I can apply the logic in other circumstances"
I don't think logic helps here.
At first glance all three words, as you say, "appear" to mean "therefore", and it seems to be more a hairsplitting exercise. Not so. This is a test of knowledge of the basic meaning of root words in a compound.
Let's take each word in turn.
于是 We all know 是 means "is", "yes", "correct" Not much help here for our problem. But what does 于 means fundamentally? It means many things in different context, but "therefore" is not its default meaning. It is more a kind of preposition, like, "for", "at", "when" So, intrinsically not suitable for our purpose as it seems more suitable for "future" course of events then a "follow-on" from past causes.
因此 This is more complex. 因 is "because", "the reason for...", and 此 is just "that", "this". So 因此 becomes "this is because" But in our problem the actions follow the past behavior of the baby, and 因此 implies some "future causes / actions", not past. It appears closer for use in our problem then 于是, but still does not "sound" 100% right.
所以, 所 -- "in such a situation / event", and 以-- "in accordance with / accordingly", so together we get "in accordance with such a situation / event". Sounds more like what we want as the baby's past behavior, (situation / event), requires taking certain future actions in accordance therewith.
So, of the three possible choices, without splitting hairs, perhaps 所以 is appropriate. Also, generally, "therefore" is the default meaning when translating 所以.