Yes, though come to think of it either definition would allow you to travel West from Ecuador to Singapore and then turn around, never visiting Indian or Atlantic Oceans. Adding the requirement “Visit every meridian” is insufficient since it allows you to start from Antarctica, circumnavigate the Arctic and come back, never visiting the Pacific.
Back to the drawing board. :dubious:
ETA: Perhaps the key is to intersect each great circle twice. :eek: