We just cut down most of a very large banana tree from a very narrow side yard. How do we get rid of these moist stumps?

I'd just take a hatchet to them, then add some sugars and compost, cover with thick mulch and water now and then. Should rot nicely, especially in this heat.

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Shepherd of the Trees
It is not our part to master all the tides of the world, but to do what is in us for the succor of those years wherein we are set, uprooting the evil in the fields we know so that those who live after may have clean earth to till.