There is something that bothers me.
"Tips & notes" gives us three examples of exceptions where "att" is used (gilla, hata and försöka): "Jag försöker att lära mig svenska." But here we have "Jag försöker se adressen" (without att), and we have indeed an explanation (https://www.duolingo.com/comment/7075383) that says försöka doesn't take "att".
What may explain this apparent difference (to me) between these two explanations?
I've removed the example with försöker att from the T&N. It isn't exactly wrong to use att after 'försöker', some people say it that way and it's an accepted answer at least in this case. This is changing over time and having an att after försöker is more acceptable now than it used to be, but I would say it's a little better not to use it.
Miscellaneous question: Could "adressen" mean the other type of address? That is, could this sentence mean "I am trying to see the (Gettysburg) Address" ?
It's only ever the locational type of address. Doesn't have to be physical, though - for instance, an email address is epostadress.
The audio pronounces “se” with a normal “s” sound, not with the “sh” that “s” usually becomes after an “r”. Is that a TTS error, or does “försöker se” not assimilate the “s” of “se” for some reason?
What exactly does this sentence mean? Is there a non-literal meaning? Also, is there a difference between what @daneestone2 said and the sentence given?
Edit: from another post about att: "The grammatical explanation is that it's not used with modal verbs."
There's no hidden meaning. It just means that you're trying to see the address. Perhaps the text is very small or barely visible.
No, there is no difference in meaning or style.