I have several trees with established sod right up to the tree trunk.
They are a pain to mow around. I can only get so close with the riding
mower or the push mower, so I have to run around with the string
trimmer and take care of the rest. I hate running the string trimmer,
as they do not make one that I can operate without crouching and
killing my back.

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.