The only way I can figure to mulch these trees "the right way" is to remove all the sod from around the roots, install a border, and fill with mulch.
These trees have lots of roots near the surface, and digging out the sod is going to be tedious at best, with impossible being the most likely scenario.
Installing one of those plastic flush-to-ground borders will be even more fun, as I will have to scribe and cut clearances for all the roots all the way around the tree. I don't want to trade one weed- wacking job for another, having to trim around a raised border.
Can I just mark a circle, spray the sod with Roundup, cut in an edge about 18"-24" from the tree trunk, and dump a bunch of mulch on it? I don't want to kill the trees.