Good question. In general, you want to inoculate about a month after it has been cut. That way, like you said, the anti-fungal compounds have died off, but other fungi have not yet invaded.
Has anyone tried boiling the resins out of conifer sawdust and trying to grow mushrooms in that? You could get all sorts of gums, resins, tars and cleaners from the various conifers and get a good mushroom substrate at the same time … I suspect. Get rid of the anti- microbial stuff and you should have a descent mushroom substrate.
To make mushroom kits and in some ways to grow the mushrooms from bags, they could do that. It may be beyond the scope of your average home based hobby mushroomer.