Gideon wrote:

I inherited many well established Concord grape vines which a previous
owner had planted about 35 years ago. For several reasons, I would like
to cut these plants as low as possible and allow them to grow back.
(These vines were never properly trained; I need to replace portions of
the fences that the plants are growing upon; etc.)

Is this reasonable and are there any special steps I should take? I do
not want to start new plants from cuttings or from purchased plants. The
existing plants have great established roots systems which I would like
to utilize.

Gideon

Should work fine - Just wait until dormancy to prune.