I have no experience with shiitake, but I managed to innoculate alder logs with oyster mushrooms using plugs. I didn't spend a lot of time with it and just left them laying in the forest. Last summer I found some dried out oyster mushrooms that i missed harvesting. I am not sure the mycelia survived last winter, which was quite cold, but may find out this summer. I think it would have gone better if I'd put the logs in straw or something and kept them more moist and off of the forest floor. I'm afraid the native fungi have moved in to the logs now. I also had a good batch of oyster mycelia going in coffee grounds in a plastic bag, but that also spent the winter outside and doesn't appear to have made it.
Alders also can give a lot of sap which I have read can be made into syrup like birch syrup (they are both in betulaceae family). I once had to cut a pretty big alder for a construction project I was paid to do and noticed that in the spring the stump was giving gallons of water every day. Now that same stump is slowly growing back little shoots. Its probably a different species than yours that we have here- ours is a crooked, curvy, multi stemmed shrub to about 9 meters maximum; over time they form a big globe shape and the very old ones have big, nearly horizontal stems that are fun to play on.
We also harvest fallen alder leaves every autumn and cover our raised beds with them and also use them to make a new "compost" (read 'moldering') heap with alternating layers of our kitchen sludge we toss in a hole all year and the alder leaves. Many people here dislike the alders because of their growth habit and tenacity. I love them for so many reasons: they are vigorous but not so tall that they shade the landscape, they can be pollarded or coppiced (though close coppicing can kill them), they are good for firewood and mulch, the logs rot quickly and don't acidify the soil like spruce, they are beautiful, and the really old ones create an amazing kind of 'spooky forest' with tunnels. They are perfect borders for gardens and fruit trees- especially as a chop and drop fruit tree interplant. They are the first (along with elderberry) to colonize a disturbance and create a thicket that takes all the light and lets very little grow below, but if you chop and drop them, the conditions are great for other plants, like apple trees, to grow. My love for alders has no end!!! It looks like there is a thread about them:
https://permies.com/t/5978/alder-Alnus-glutinosa