Regarding cheery picking counties, this was tried in the Bush/Gore situation. Gore asked to recount counties that were strongly democrat and he lost by 500. If he had asked for the whole state, he would have won.
There were some articles written where a liberal reporter investigated the votes of all counties in Florida and he had to ruefully admit that even if the whole state was recounted, Gore still would have lost by about 300 to 500 votes. So there were arguments(early 2000’s) countering your “whole state” view.