To reach their wedding venue, Austin O’Reilly and Iulia O’Reilly crossed a swaying suspension bridge, trying not to glance down at the glacial river below. With each step, the bridge shook under the weight of people and yaks. Mr. O’Reilly, 25, had seen similar bridges in the 2015 movie “Everest.” Now, he was on that titular mountain with his fiancée: walking a precarious bridge, crossing jagged moraines and traversing rocky terrain on a nine-day trek to the Everest base camp.