This is a bit opinionated, and it's hard to be definite without seeing the full quotes, but here's an analysis. TLDR: Italics could be arguable for 'fortissimo' and either italics or quotes or neither for 'Dies Irae'.
There are two reasons for italics relevant to us now. 1. Titles and 2. foreign words used as if they were English. Likewise there are two possibly relevant reasons for quote marks: 1. direct quote and 2. reference to the words themselves rather than the concept they represent.
It's arguable that fortissimo should be italicised as a foreign word. However you say that the writer elsewhere chose to use italics for musical titles, and she may have felt that to also use it for fortissimo would be confusing. Fortissimo is well-used enough to be considered an English word.
Dies Irae might well be, and often is, the title of a piece of music. You might write "Mozart's Dies Irae" and use italics to indicate the title. However here "Dies Irae" is not being used as a title - it is being used to refer to a particular kind of musical composition. Talking about "a 'Dies Irae'" indicates this. As such it wouldn't deserve italics. Almost invariably those pieces have the title Dies Irae, so italics might be justified - however again, having used italics specifically for a title elsewhere, the author might decide using them here might be confusing. The author might still want to separate the 'Dies Irae' from the rest of the text, so quotes is justifiable.
To answer your question at the end - yes it is sometimes better to violate the strict rules in order to achieve clarity, and it seems that is what the author has done.