I've been appealing to everyone I can think of for a definitive answer to this
question:

- are there any undocumented methods or workarounds that would let you
reliably seek intervals of less than one second in an .flv file?

Ideally, I would like to be able to step ahead one frame at a time. The
seek() method will only look for the nearest keyframe. Even if I create a
video file where every frame is a keyframe, the seek method seems perfectly
happy to find any keyframe within the nearest second - in other words; it fails
if I try to seek within one second of the current playhead position.

Any thoughts?

It's worse than that, I'm afraid. Even if every frame is a keyframe,
netStream.seek will fail if I try to seek a point within one second of the
current playhead position.

There has to be a way to address this. I spoke to Macromedia tech support
today about using Director instead, but they felt that the performance would be
very poor with more than one movie visible on the stage at a time, (this isn't
a problem with .flv videos). They said that I would have to disable the
Director stage property for the video in order to position sprites above the
video in Director, and that this owuld impair performance.

I would prefer to build somthing entirely in Flash, and I know that it would
work, if I could only address the issue of playhead positioning and somehow
allow users to advance frame-by-frame.

Maybe you are doing something wrong. I just followed every step and it works
perfectly. First I created an flv video with 30 fps and a keyframe every 30
frames. In this experiment everything went as expected and even though I made
time increment of 0.01 the frame will not change until it is close to one
second.

The I took the same video and re exported as having a keyframe every 1 frame.
Tested my movie again and everything works as expected too. Every time I press
the button a single frame is shown in my screen.

I don't know what is going wrong in your project.