I would make an argument for a proper godswood in BWK as opposed to a garden. Godswoods would be signs of heritage and wealth, and all canon indicates houses try to have them whenever possible. The Arryns attempted to put a weirwood in the Eyrie despite being fully Andal, a godwood was put into Harrenhal despite the Hoares believing in the FotS, the Targaryens put a godswood in the Red Keep despite having no connection to the First Men, etc. The fact that HIghgarden and near every other great castle in Westeros still has its godswood is a sign that it's fashionable. Also the Florents are known for claiming their First Men heritage and connection to the Gardeners as why they are more fit to rule Highgarden over the Tyrells; a godswood would show this lineage. IMO the only places where not having a godswood would be common are places where they're unable to grow or were conquered by Andals, neither of which apply to the Reach.
On a more meta note, this server focuses highly on realism over fantasy. Godswoods are the one canonical aspect of castles in ASOIAF that make them purely Westerosi and not just European. They are a way to undeniably tie castles to ASOIAF and I think that's a good thing, especially for an important castle like BWK.