an icepick through the keyhole

One thing you need to keep in mind about the Faction Paradox universe is that the Faction Paradox you read about in the BBC books and the Faction Paradox you read about in the Mad Norwegian Press books (and everywhere else) are not precisely the same.

Lawrence Miles created FP for the Doctor Who universe, but after a point disagreed vehemently with what the other writers and the editors were pushing FP to be. By the time the FP storyline in the books ran its course and ended with the destruction of Gallifrey in "The Ancestor Cell", Miles had basically left the project.

So all the stuff he did with FP outside is spun off from the same continuity as the BBC books and even uses some of the same characters that Mad Larry created for the line, but at the same time it's more properly an alternate universe (I believe Mad Larry rejects the FP as portrayed in "Ancestor Cell" as an abberation and it's not part of his continuity).

For example, while Mad Larry intended Grandfather Paradox to be a future incarnation of the Doctor, Lance Parkin turned the Grandfather into everyone's future incarnation, which is a neat little twist but I'm not sure it's one that Miles would have approved of or agreed with, and is still probably not the case in his own FP stories.