Long winded idea:
I was at a garden center last week, inquiring about landscape fabric for a
small area under the eaves of my house where rain rarely reaches, and
nothing grows but weeds that like desert conditions. I don't have time to
research & plant something nicer until September. The store owner said "If
you're gonna put mulch on top of the fabric, use this kind. If stones, you
want this stuff - it's practically impossible to damage".

So...the OP might want to consider some high quality landscape fabric, too,
even if he uses it to make some sort of wrap over the stumps, as opposed to
laying it flat. It would be far more durable than plastic.