Thank you. I did some further research. A search on the internet for “per ianuam” gave several results:
Miraculosus Christi per Ianuam clausam ingressus: this is the title of a book containing a sermon.
Marcus per ianuam (in hortum ad equum) currit: from a grammar site.
Qui non intrat per ostium in ovile ovium, sed ascendit aliunde, ille fur est et latro: from the Evangelium secundum Ioannem, 10.1 and .2
However, I’m still wondering about the second variant, i.e. using an ablative.
Having a look at A&G’s New Latin Grammar, I do not think that such an ablative would be an ablative of the way by which (A&G, sect. 429.4a) as that seems to imply some spatial extent of this “way” which is not the case with a mere doorway.
It could be an ablative of Means or Instrument (A&G, sect. 409), but the examples given by Allen & Greenough do no fit exactly. Nonetheless, Aedificium posticâ intravit feels good (I guess, I have developed a slight weakness for the pure ablative).
And Google just translated “The owl swallowed the mouse.” as “Noctuam devoravit mus.”!!!
And “scuba diver” as “Aliquam varietas” :: I have seen the old English adjective “divers” = “various” in the Bible, but how does “scuba” become “aliquam”!?!?
“The cat scratched the dog.” became “Cati scratched canis.”.