grammar - あまり meaning "too much"

When using あまり in the sense of "too much" (as opposed to "not very"), until recently I had always seen it as あまりにもA, with A being the thing that there was too much of. I never really tried to relate the meaning of individual particles に and も to the word あまり and try to understand how it takes on the meaning of "too much", I just accept it as a set expression. Here is an example of this usage:

• あの本はあまりにも面白かったので、読むのに夢中になっていたら、いつの間にか夜が明けていた。

Recently I saw it used as のあまり and あまり with seemingly identical meaning. Examples:

• 母は、私を心配するあまり、体調を崩したようです。


• その犬が死んだ時、先生は悲しみのあまり、しばらく仕事を休んでいました。

Is this the same usage of あまり? Could I simply switch to the other pattern in all 3 of the above examples?

• あの本は面白かったあまり、読むのに夢中になっていたら、いつの間にか夜が明けていた。


• 母は、私をあまりにも心配して、体調を崩したようです。



• その犬が死んだ時、先生はあまりにも悲しみ、しばらく仕事を休んでいました。

Is there any difference in nuance here, or perhaps is something flat out wrong? Also, is there any context in which あまり can be used with に or は such as あまりに or あまりは? If so, what is the meaning in this case? Maybe someone could construct an example sentence with translation using あまりに and/or あまりは, if it makes sense.