Quote Originally Posted by PsiLord
...while it might be used with a Perfective verb to convey the idea of punctual impossibility, hence my trying it with both types of verbs just to check what it might sound like.
That it true to a degree. For example, you could say "Эту книгу нельзя прочесть/прочитать", and that would mean that it is impossible to read (although I would prefer to say "Эту книгу невозможно" прочесть).

Quote Originally Posted by PsiLord
Based on what I'd read, I confess I did think it might mean something like 'I can't finish reading this book (because it's too difficult for me)' — what could it be better expressed like then?
You could say, for example "Я не могу прочесть эту книгу" (I can't read this book), or "Я не могу дочитать эту книгу" (I can't finish reading this book).


Quote Originally Posted by PsiLord
Ah, and just in case, the two examples I had were the following:

Тут нельзя переходить улицу. (Impf.)
Сейчас нельзя перейти улицу. (Pf.)

Would the sentence with the Perfective verb be correct in this case?
If somebody is standing with a friend at a crossing and the traffic light is red for them, they would normally say "Сейчас переходить нельзя". (Meaning that it is forbidden and/or dangerous).

If you want to say that it is physically impossible (because of heavy traffic or something), you can say "Сейчас перейти улицу невозможно/не получится/нельзя".