Wendy,
I'm euthanizing a bunch of sweetgums, which I would assume to be a fantastic pollarding tree, but they spread via the
root and are a primary colonizing tree here. My technique takes 2 years. Year one I ring the tree with a chainsaw as low as I can get without dulling the chain- hopefully low enough to bush hog over. This prevents the tree from sending sugars to the
roots in the winter, but
water can still go up and transpire. I'm not familiar with your species at all so not sure how applicable this is.
Year two the trees get cut generally a little above the ring, and I drill a few holes in the stump and cover with compost and mulch. Often the
chickens perch on them and
poop on the stumps. The tree trunks are perfect for
mushrooms because they maintain a high sugar content even in the winter, so off they go. It takes, as Travis says, a couple years to degrade but that depends on the diameter. What is cool is that in this climate the same year you cut them you can see where the roots were because they will generally send up fruiting bodies from whatever fungus has colonized it. I no longer plan on taking the roots out at all, let the fungi do the work.