I'm also inclined to argue that government run monopolies are all inefficient, but to different extents, and so using them to estimate costs is highly questionable.

This is getting into politics, but...

There have been many empirical studies examining the efficiency of government bureaucracies versus business in a variety of areas, including refuse collection, electrical utilities, public transportation, water supply systems, and hospital administration. The findings have been mixed. Some studies of electric utilities have found that publicly owned ones were more efficient and charged lower prices than privately owned utilities. Several other studies found the opposite, and yet others found no significant differences. Studies of other services produced similar kinds of mixed results. Charles Goodsell is a professor of Public Administration and Public Affairs at Virginia Polytechnic Institute and State University who has spent much of his life studying bureaucracy. After examining these efficiency studies, he concluded: “In short, there is much evidence that is ambivalent. The assumption that business always does better than government is not upheld. … When you add up all these study results, the basis for the mantra that business is always better evaporates.”

Source.

"a lot of America's ridiculously expensive healthcare is a result of inefficient use of resources, and dodgy incentives, and such things. "

Given Alcor is based in the US, and has to rent time and labor from the medical profession writ large, I'd suggest that overcoming those obstacles would indeed result in a fairly substantial savings for them. Alcor is small enough to suffer rather heavily from inefficient use of resources - they do maybe 10 vitrifications per year, but have to have the staff and supplies ready to go 24 hours a day, 365 days a year.

Also, the idea that doubling your size decreases costs by 10% is plausible, but dubious over 17 doublings.

I'd honestly conclude "insufficient information" here. The history of computers in the last few decades makes a mere tripling in productivity look excessively pessimistic. On the flip side of the coin, equipment and labor costs run in to hard limits. I can certainly see a 200% productivity increase being optimistic, but I can also see it being pessimistic. Since I don't know, it felt safest to just run the numbers as current research suggests, without adding new assumptions :)

That said, the best defense I can give for those numbers is that I was trying to be optimistic, because my starting assumption is that there's no way you're going to finance universal cryonics in today's political climate. I didn't want to throw myself up against an easy version of the problem :)