"Pavel314" writes:
However, growing season continues on for a couple of months. Is there any
way to encourage the potato plants to hang around until early October and
maybe produce a few more tubers?

I think you'll find that potato plants die down when they are ready,
even when the growing season continues. You need to plant some
later in the season if you want to harvest later ones. Before
harvesting you don't have to wait till the stems brown off. You can
scratch around the boundary of the expected tubers and gather early spuds
if you want some for eating; don't damage the plant or remaining potatoes
and these will continue growing. You only need to wait till the plants
brown off if you intend storing the harvested crop.
--
John Savage (my news address is not valid for email)