Tonight I tested this further to see if the setting in "Power Options" was really the culprit. I found that it is, and the behavior is completely reproducible.
The procedure I used to test is simply to change the power setting, put the computer to sleep, wait a few seconds, wake it up, and run the speed test. I'm on battery the entire time, and never changed physical location (I'm about 8 feet from the wireless router).
At “Medium Power Savings” I get results like these every time. You note from the upload speed that the connection seems to recover briefly sometimes but often then drops again.
At “Maximum Performance” I get this. Consistently very speedy.
I'm a scientist, and I've repeated this enough times that I'm fully convinced that changing the power options can make this problem disappear. I hope it works for others.