I agree with you that SIN -> ATL (via SFO) is your best bet in terms of travel time, it's the most direct and heaven knows how well they would handle even longer travel times with additional connection points, etc. As a 30 year old who has taken my fair share of long haul flights in Economy on a variety of airlines, I can tell you with certainty that they all suck. That being said, UA IMHO has the best seating options with E+ since on the long haul jets you can often find a row that is at least not cramped (i.e. emergency exit row where you can stretch your legs out fully). Sadly, United charges an arm and a leg for those seats if you're not elite (if memory serve me correct around $300 USD/person for the plush seats)
One of the concerns travelling long haul, especially at an older age is the risk of DVT that can occur when you have blood pooling around your leg for several hours while you are seated for such long periods of time. A nice pair of compression socks and/or moving around the cabin every couple of hours can make a real difference.
In terms of other booking options you may want to check to see if Singapore Airlines has any award availability as it's my understanding that they are transfer partners with a variety of credit cards. I suspect flying Singapore Premium Economy to New York or San Francisco will be a heck of a lot better than flying United/AA/Delta. Your parents could then catch the Singapore Airlines flight down to Atlanta from SF/NY (operated by United Airlines).
Hope that provides some insight.
Safe Travels,
James