Do any bosses outside their zone, drop their drops?

Solution 1:

After testing from the asker, it appears that the wiki may be wrong. However, this is still the most thorough answer so it will remain until more testing can be done.

Based on my research, I'd say that yes, it is possible to get these drops in the area you mentioned by killing the bosses, listed here on the Fandom page for the Pheasant Feather, here for the Black Deer Leather, and here for the Boar Tusk.

This answer is specifically referring to

Amagaeshi Shrine

I found a post on Reddit linking to a Japanese Wiki for the game detailing the drops for the area. I'd include the all drops here, but the tables are too massive so I'll just include the few I believe to be relevant. It states that

levels 55 and 60

have a rare drop of a Boar Fang (which I believe to be a Google Translate issue), or Boar Tusk. It also mentions a Hakuchi Feather which I believe is a mistranslation for Pheasant Feather for these floors as well.

I also found the Fandom page for the area, and it lists Pheasant Feathers as possible loot, as well as Boar Tusks. There is also a post on Gamefaqs mentioning one of your concerned items in the area as well:

floor 11-15 for boar tusk chance