This seems like a promising direction. So let's say that by religion I mean a useful meme. The meme consists of a doctrine. That is, a collection of statements regarding human belief or action. A person infected with the meme lives in accordance with the doctrine. The doctrine is designed to cause a useful effect, apart from its own flourishing. The effect is caused by changes in behavior of the people infected by the meme. The effect need not be explicitly stated within the doctrine. This a broad definition of religion, as it doesn't require that the doctrine contain any statements about the supernatural. But at this point I want to keep things open. As some posts have suggested, there's a lot of argument about what does or doesn't constitute a religion.

In order to be successful, a useful meme must be sufficiently:

1. Transmissible, meaning that it must be pragmatically possible to expose many people to the meme.
2. Infectious, meaning that a significant number of people exposed to the meme must become infected.
3. Contagious, meaning that it must spread of its own accord, until it has infected a threshold number of carriers. The threshold may differ from meme to meme, and is whatever threshold is needed to enable the successful creation of the desired useful effect.
4. Viable, meaning that it must be possible for a person to survive and prosper when infected with the meme.
5. Robust, meaning that once a given person is infected, it must resist eradication within that individual.
6. Hardy, meaning that it must be able survive, and possibly flourish, in a variety of intellectual environments, and there must be no commonly found environment in which it cannot survive.
7. Resistant. Meaning that beyond a certain degree of spread, there cannot be an obvious method by which a (presumably non-infected) person or group can eradicate it.
8. Stable, meaning that it must not change its nature significantly over time. Changes that continue to allow it to flourish and to cause the desired effect are permissible.

This list is not meant to be definitive or exhaustive. And I don't claim to be using the best terminology.

For example, some religious doctrines contain the idea that if you cease to believe in any part of the doctrine, you will suffer in Hell upon death. This idea might enhance the robustness of the religion by discouraging the development of disbelief. Others contain the idea that it's your duty, or that you're rewarded in some fashion, for converting non-believers. This idea might enhance the contagiousness of the religion by encouraging those who are already infected by the meme to work to infect others.

Using this framework, perhaps the original post might be improved a bit. Putting some of the questions asked in the original post into the new framework, we get:

1. What useful purposes does religion serve? That is, what kinds of "useful purposes" can be designed into such memes?
2. Are any of these purposes non-supernaturalistic in nature? That is, can a completely non-supernatural religion flourish and create a useful effect?
3. What is success for a religion and what elements of a religion tend to cause it to become successful? That is, what elements of currently existing religious doctrines have helped them to become successful?
4. How would you design a "rational religion", if such an entity is possible? That is, is it possible to design a religion that encourages "less wrong" cognition?
5. What are the relationships between aspects of a religion, and outcomes involving that religion? For example, Catholic doctrine includes elements that discourage birth control. Lack of birth control encourages higher birthrates among Catholics. This encourages there to be a larger number of Catholics in the next generation than would otherwise be the case. Thus the toolkit now contains one element: the prohibition of birth control as a means of increasing the contagiousness of a religion.
6. How do aspects of religion cause them to evolve differently over time? For example, Catholicism contains a permanent, authoritarian hierarchy of individuals who are dependent on the church for their survival and satisfaction. Without the Church, a Cardinal with no other job skills might starve or suffer disrespect from the community. Thus he is incentivized to increase the authority of the Catholic church in order to help secure his own survival. Over time, Catholic doctrine adopted the idea that the Pope is infallible. It might be possible to draw a line between the two phenomena and say that in a doctrine which supports a social structure that includes a permanent, authoritarian hierarchy of individuals who are dependent on believers for their survival and satisfaction, the doctrine will tend to evolve towards the accumulation of power for the hierarchy so as to ensure and increase their survival and satisfaction. Possibly another element for the toolkit.

What other such heuristics exist? Would a large enough collection of such heuristics aid in the analysis and design of religious movements?

but it seems like you guys are generally intelligent

Nah, we just fake it :-P

Since whatever fills at least some of these roles will attempt to expand to fill all of them.

In the real world I don't see that any religion tries to fill the same roles. Christianity doesn't try to expand to fill law-making in the same way that Islam does.

the purposes served by religions are better served by what other social constructs?

The secular parallel to religion is called an ideology.

What does "better" mean?

Unfortunately, I can't give a good definition for this except by example. Christianity, Judaism, Islam, Buddhism, Daoism, Hinduism, Atheism. I suppose that it might even be possible to ask the questions assuming that science is a religion. The focus of the questions is intended to be on the engineering and social aspects, rather than on a question like "Should Atheism be considered a religion?" I understand that the vagueness makes this a less than perfect delineation of a topic.