It is my impression that what she was eager for was not the flying itself, but to do it while it still had enough publicity value that could be monetized.
After her long-distance record flights in her Vega in 1935 she recognized that the days of private venture aviation record-setting were coming to a close. The few records that remained to be set required larger aircraft far more expensive than she could afford and there was increasing pressure for the government to shut down stunt ocean flying. She removed the special fuel tanks from the Vega, entered into a charter/flight instruction business deal with Paul Mantz, and accepted a part-time student advisor consulting position with Purdue University. It was Putnam who saw Purdue's infatuation with Amelia as an opening to get her a new airplane with which she could continue to make headlines - and money. He sold Purdue on the idea that what Amelia wanted was a ship with which she could do genuine scientific research such as high altitude flying. A world flight was mentioned only as a possible finale to a program of research flights. Amelia affirmed that ambition in interviews, but what she really thought is hard to know because she did not write about it in private correspondence and she was never hesitant to mislead the public when it suited her purpose. If she was serious about wanting to do scientific research, it was an unrealistic pipe dream. She had neither the education nor the skill required for developmental test flying. Putnam's letters make it easy to know his motives. From the beginning, his focus was on a world flight that "would put us on easy street."
By the time she got to Oakland in March, the world flight had already proved to be far more complicated and expensive than anticipated. Her disillusionment is reflected in her "one more good flight" comment. The debacle in Hawaii made things that much worse. Had she quit then, her reputation - and her prospects for capitalizing on her fame - would be in tatters. There is no evidence Putnam pressured her to try again. Whether prodded by pride or practicality, the decision to keep going was hers.
What he said.
I remembered this from Finding Amelia.
It occurred to me, in reading this thread, to consider what if she had never attempted the world flight. She was already famous, could already get paid to appear, and had the faculty position at Purdue. This might have been enough for some people. For her (or Putnam, or both of them) this was not enough. She wanted one last big accomplishment to put her "on easy street" for life.
Then it occurred to me that the world flight around the equator would be one thing she did first, not merely being the first woman to do what a man had already done, as were her previous flights. As "Lady Lindy," she had always been following some man, while Lindy did things no one had done before he did. That alone, which could stand on its own merits as a flying achievement, could be enough to make it worthwhile.
Don