Mountain Ash tree full of oysters

2 years ago I cut down half my dad's mt. ash tree and for the last 2 years the "firewood" has been giving me oyster mushrooms. Now there are very small mushrooms growing on the tree situated in full sun. Hes ready to let me cut the rest down to set in the shade and let fruit. Heres the rub, oyster season is over here. Should I cut it down now or wait until early spring when the tree is dormant?

How much of the wood have the oysters already eaten? If it's far gone, you could cut it down, use it as hugulkultur, or burn it. If it is not much eaten, I would keep it and let it produce more oysters in the spring and in the fall next year.
john s
PDX OR