Thanks, all, for the advice.
I think I am going to pass on the resodding for now. Not yet entirely
sure whether I go with the nuke and replant, or nourish what's there
with overseeding. I think I'll speak to the lawn rep about what the
odds are of nourishing and building on what's there - although there
doesn't seem to be much there. I have the patience, and some money, but
little time to devote personally. What personal time I do have
available is being used weeding and feeding the new hedges, shrubs and
flowers. One problem is the lawn care company which looked at things
(Nutrilawn) is not a landscaping company. They'll kill weeds and add
fertilzer, do core aeration, etc. etc., but they don't do seeding or
sodding so I'll have to check out a landscaper interested in a small
job.