Of course there is a way, involves technology and a speedy vehicle, better if it flies.
You can not use star locking navigation, since on FE stars also make a circle, if you follow a star you make a circle around North Pole.
But you can use the old and good magnetic compass, even electronic ones (much more precise), and also, you can use electronic accelerometers, electronic gyros, they are very very good, much better than the old mechanical ones used on rockets. One of my jobs is develop field products using those little high tech devices, they work very very good. As a matter of fact your own Android of iPhone has all of the above and even more of those little gizmos that you never heard about.
You don't need too much, just depart from New York, for example, towards North+330° (30°NW), calculate a formula (based on RE) to go straight around the globe, so you would return to New York from the South. The formula will be a simple navigation based on magnetic North deviation versus distance traveled, that is very simple, used for centuries. That circumnavigation straight line will cut the globe in two, slicing close to the North and South Pole.
Why use de 30°NW instead of flying directly over the North and South Pole in a straight line? Because, by doing so you can keep track of where is the North all the time, no matter where you would be. If you fly over the North Pole you can not compute your bearings very well when over the poles, some may say "oh, you make a turn and don't even noticed" .
Following 30°NW from New York, you will fly over Canada, probably China, Australia, South Pole (FE ice wall), then magically appears over the tip of South America - Argentina or Uruguay, then over Brazil, back to New York. The "magic" here is the fly distance and time from Australia to South America over the South Pole would be much shorter than one can see on FE map. And that is not from winds, light refraction or any other magic you can pull up from the sleeve, it is plain real distance. May be you can use the
to plot this trip.
The problem is that you can not have a fly object that can do such trip in one fuel tank. I think only a B-52 can do 14~15000 km between refuels on flight, and complete the circumference with at least 3 refills.
But wait, thousands of orbital satellites do it all the time, but no, FEs don't recognize the existence of orbiting satellites.
But there are an easy way, a flight from Sydney to Montevideo (Uruguay), 11862km, 25 hours flight (wristwatch time), one stop in Arturo Merino Benitez Airport in Santiago Chile. The tarmac waiting time in Chile is 11 hours, so the Qantas flight time is a little bit short of 15 hours, average speed of 790km/h (493mph).
https://www.prokerala.com/travel/flight-time/from-sydney/to-montevideo/On FE world, it would be more than 35000km, to make it in 15 hours, the average speed would be 2333km/h, it would required a Mach2 airplane to complete such trip in that time. Even the Concord at 2180km/h at 60000 ft (18000m altitude) would not do it in 15 hours, with a maximum range of 7200km with the 210000 lbs of fuel, it would need 5 refueling stops during the trip.
FEs would say that flight doesn't exist, it is a lie promoted by governments and the potential travelers aboard were paid off to lie.
If you want to book such flight, click here:
https://www.tripadvisor.com/Flights-g255060-o294323-Montevideo_to_Sydney.html