Thanks, Randy, the site works very well!
Unfortunately, it gives me answers I don't want to hear: The most likely routing,
AUS -> DFW -> JFK -> LHR
comes up
10,028 miles RT.
Stopping at STL is a little worse, at 10,092 miles.
Stopping at DCA works, at 9926 miles, but there is only one flight per day.
I wonder if taking the non-stop AUS -> LGA flight, then surface transportation to JFK, would be permissible? It's less than 9920 miles.
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Middle_Seat