Kentucky Coffeetree (Gymnocladus dioicus) - inoculate with edible mushroom spore?

I can't seem to find any information about inoculating Kentucky Coffeetree for edible mushroom production. Does anyone have experience growing mushrooms such as shiitake on this tree's wood, or have a reference for what types of mushrooms would be best suited for it?

I'm about to use some oak for my first attempt at shiitake, but also have some sizable Kentucky Coffeetree limbs that I was going to use the extra spawn on (or buy a suitable spawn for) - unless it's a lost cause. I know Black Locust is said to be not very good for mushroom growth because it's so rot-resistant, and I'm wondering, because Kentucky Coffeetree is a legume that it might have the same sort of situation...

Any feedback would be great. Thanks.

In nature Ganoderma root and butt rot grow fairly readily on these trees. I would think that you could use fresh, uncontaminated wood of Gymnocladus dioicus as a medium for growing Oyster mushrooms. Inoculate just as you would White Oak medium.