Is it grammatical to combine in and advenire to say, for example, in Finniam advenit? This sounds otherwise fine to me, but I'm slightly worried about mixing the prepositions in and ad so I want to check.
Yes, this is an attested usage. Lewis and Short should be your first place to check for such information. For advenio they specifically give the list of constructions "absol., with ad, in, or acc.", and cite several examples with in. Here's an example from Cicero, Philippic 11.30:
quamcumque in provinciam eius belli gerendi causa advenerit
"in whatever province he arrives for the purpose of waging that war"