The Conifer Coral, Hercium abeitis, grows on pines and would be a good candidate for inoculating pine stumps.
I have seen this mushroom growing from partially submerged logs. The fact that it enjoys this habitiat leads me to believe it would be happy growing from stumps. Literature from places that sell plug spawn for this mushroom (Fungi Perfecti) support the theory.
The Conifer Coral is from the Hericium family and is related to the Lions Mane which is a beatutiful mushroom also. They are both choice edibles and are easy to prepare.
I am going to spread this mushroom around to some pine stumps this year. There are plenty to inoculate with the pine beetle kill. I encourage you to do the same.
When would be the best time to inoculate? When to start looking for flushes?
The best time to inoculate is between March and October. It typically takes 9 to 12 months for the mycelium to colonize the stump. After total colonization, you should see flushes when the conditions are right. The beauty of it is, they will flush for years. I think inoculated plugs are the way to go for stumps. Fungi Perfecti sells plugs and plug kits.
I have found Conifer Corals in the fall, and not many. This is the reason that growing them for myself, or at least spreading them interests me. The ones I have found were on old logs close to water, or partially submerged in it. They are tricky to find as the mushrooms grow from the sides of the log, and are not very large. Growing from stumps would make finding and picking them much easier! It also would let us know when to look for wild flushes.