First, let's clarify what we are talking about.
(A) indirect passive with a transitive verb
(B) indirect passive with an intransitive verb
(C) "direct" passive with a transitive verb
Note that only (A) and (B) are usually called suffering/adversity passive (迷惑の受け身). (C) is usually not called adversity passive even if the event is unfortunate to someone. And importantly, when an adversity meaning is present, the event is unfortunate to the person marked with は.
Am I correct in saying that the sentence patterns with transitive verbs of both adversity passive and simple (direct) passive are identical?
If you mean the difference between (A) and (C), no, their basic grammar patterns are different, as you can easily see from the examples above.
(This may be nit-picky, but when words are heavily omitted, (A) and (C) can appear identical. For example, 彼に殺された can mean both "[I] was killed by him" (C) and "[I] got [my daughter] killed by him" (A) depending on the context.)
how would one know whether they are simply stating the facts (simple passive) or describing unfortunate events (adversity passive)?
In the case of (A) and (B), they
always almost always describe events which are unfortunate to the person marked with は. In the case of (C), it purely depends on the context.
With the above two example sentences, could I convert any one or two or all the verbs to passive depending on which verb or verbs are deemed as an unfortunate events?
In general, there can be two or more indirect passive expression in a single sentence. There is no particular restriction. But in the case of your frog story, I feel there is no place to use indirect passive.
虫はカエルにごくんと飲まれました is fine if this were the story about the worm, but the main character of your story is the frog. It makes little sense to suddenly change the topic and form a sentence like this. The misfortune of the worm is not the author's concern. (Or are you trying to rewrite the entire story from the standpoint of the worm? That doesn't make much sense to me, either, because the worm is already dead when eaten.)
カエルにお腹が空かれました is wrong in this context. It means something like "[I] got bothered because the frog became hungry." When this event is unlucky to the frog itself, you should say カエルはお腹が空いてしまいました.
What is this supposed to mean? This sounds like "It appears to me that I am planning to be bothered by someone's nap"...