I had not realized the Stack Exchange post was yours. Good work.

New research into short polyphasic sleep is not so interesting to me. I think it is plausible that a polyphasic schedule could modestly reduce sleep requirements (perhaps around 1 hour at most) by reducing the duration of lighter stages of sleep (but not eliminating; it's not clear these stages are unimportant). But that's not what people interested in polyphasic sleep are testing. Instead, they try very short schedules that don't make sense. I skimmed through puredoxyk's original post on polyphasic sleep and it seems she decided 2 hours total was right because that was about as much REM sleep as she was getting before. This goes back to problems mentioned elsewhere: REM is not the only important sleep stage and nap-type sleep schedules don't produce purely REM sleep. I'd like to see a change in research direction among polyphasic sleep proponents towards longer schedules.

Phrases like "work okay" have a fairly broad meaning. There are plenty of people who think they are highly functioning but who could function a lot better.

I agree. I think many people who maintain short polyphasic sleep don't recognize how impaired they are. I wasn't trying to set the bar low. I was responding to the suggestion that I must think everyone who claims success is lying. I do think lying and exaggeration play a role, but here are some other easy justifications I can offer: acclimation (short polyphasic sleepers get used to being sleep deprived), placebo sleep effect (they think it works, minimizing the tiredness), positive publication bias (might explain why the Leverage Research folks haven't followed up), and wishful thinking. These explanations are in addition to the self-selection effect for short sleepers that I previously mentioned.

There are a number of other ways to potentially reduce your sleep need that I believe are more plausible than polyphasic sleep. I'll detail a few I am aware of.

I've read that some people with delayed sleep phase disorder find that they can sleep at times not aligned with their circadian rhythms, but the sleep is not restorative. Aligning your sleep with your circadian rhythm seems like one way to potentially reduce sleep need. The only sleep schedules that fit well with your circadian rhythm are monophasic and biphasic (i.e., with an afternoon nap).

Another thing I've found that potentially will reduce sleep requirements is meditation, but with a roughly 1-to-1 meditation-time to sleep-time conversion rate, it doesn't seem to help with the larger goal of increasing useful time awake. (But for those who like meditation, this seems like a reason to do it.)

There also are various drugs that increase deep sleep at the expense of lighter sleep that could reduce sleep requirements, however, most of these drugs are not available (e.g., ritanserin is not produced on a large scale, and GHB is highly regulated) and/or unattractive for other reasons (side effects, cost, half-life, toxicity). Stimulant drugs also are options during the day, though, they won't make your sleep more restorative.

I've also done some research into the effects of physical exercise on sleep architecture and wakefulness. Exercise can increase deep sleep. It is not clear if this effect is larger than the increase in deep sleep required to repair your body after exercise, though anecdotes in the article suggest that people believe it is (I am unsure). Also, physical exercise does not appear to wake you up for very long and likely will make you more tired until you go to sleep if you are sleep deprived.

Another idea I've had involved applying optimal control theory to mathematical models of the sleep cycle, but I suspect this will just tell you to sleep at times aligned with your circadian rhythm.