So what to do with the tengu village, eh? We need to choose between asking our way through and sneaking our way through.
Asking's a fairly simple affair. If we're lucky, we draw 'Miz, who remembers we helped get a picture of Aya, and thus may be ever so slightly more lenient about letting us through. Regardless of who shows up, we're here to investigate and potentially solve the mystery, we're more or less working with Reimu on this task, and we have the trump card of being "backed" by a whole boatload of oni who are our acquaintances-if-not-friends and far more shitripped about what has happened than any other group of people we've come across yet. I'm sure the tengu will need to think twice before hindering an investigation being carried out by the first person to try to restore normality to daily oni life. Even if this fails, we can double back and try to sneak in, or we can request Sanae come meet with it.
Sneaking in requires no negotiation but has its own list of problems. Two-and-a-half feet is rather large for a fairy, and we're not terribly well-equipped for the transformation clothing-wise. We might be able to use the rabbit dress, depending on how big it is, but any particularly traveled tengu may recognize the origin of the outfit and call shenanigans, as rabbits aren't exactly known for their honesty. (That we aren't a rabbit won't make a difference because we'll still be a trespasser.) We'll also look awkward as all hell carrying the purse and trident around, both in terms of size and in terms of where the hell did a fairy get all those things. An alternative option is to stash our stuff somewhere that won't get nicked, modify as much as we can and make the trek nude (our regular outfit might be small enough that we could try to store it within ourselves so as to not talk to the Moriya Shrine buck naked). Or use a Seed, though I'm hesitant to use one this quickly.
On top of all this is the fact that, while not being allowed in still leaves open the possibility of sneaking in, the reverse is decidedly not true. Sneaking in gets one coin; if we get busted somehow, that's that, we're looking somewhere else. I doubt the tengu would even relay any messages to Sanae if this happened.
If we want to sneak in, we need to cover all those problem areas and make sure it is going to succeed, because there isn't a Plan B along that path like there is with attempted negotiation.