What makes for a stable marriage?

It is, but thing I would encourage people to keep in mind if they're wondering whether they want to participate in such a tradition is: Your marriage will be what you make it. No particular marriage has to be patriarchal, though of course many are.

You may choose, for example, not to have the wife change her last name; or maybe you both change your last names to something new, maybe by combining parts of your names (I saw this done once). The significance of that is symbolic, of course -- it expresses your commitment to an equal marriage; it doesn't absolve you of doing the hard work to make that a reality -- but it can be an important symbol.

You also might want to take a close look at the wedding ceremony itself. Using two rings is an easy step. The old tradition of having the bride's father "give her away" is one that I would suggest you might want to omit. If you can't bring yourselves to do that, maybe you could have the groom's mother also give him away -- people will laugh, but you'll make your point. Anyway, the larger point is, it's your ceremony, and you get to design it.

Can you have an equal marriage without doing any of those things? Of course you can, but if you find yourselves resistant to symbolic actions like these, you might want to ask yourselves why, because if you resist the symbols you will very likely resist the reality.

So this article is conflating elopement with not having wedding guests. They aren't the same thing. I eloped -- got married in secret. No, there were no wedding guests. That does not mean the two things are identical.

Though, Wikipedia http://en.wikipedia.org/wiki/Elopement_(marriage) says:

To elope, most literally, merely means to run away and to not come back to the point of origination.[1] More specifically, elopement is often used to refer to a marriage conducted in sudden and secretive fashion, usually involving hurried flight away from one's place of residence together with one's beloved with the intention of getting married.

Today the term "elopement" is colloquially used for any marriage performed in haste, with a limited public engagement period or without a public engagement period. Some couples elope because they dislike or cannot afford an expensive wedding ceremony, or wish to avoid objections from parents, or religious obligations.

Which gives me pause because, on the one hand, I married in secret. On the other hand, I did not actually go anywhere and our circle of mutual friends all knew our intentions to marry for like a year or more beforehand.

We did end up divorced but we were married for more than 2 decades and the divorce was amicable. I think it lasted as long as it did and fared as well as it did in part because we handled our marriage as a very private matter. I don't think you will ever get me in front of 200+ people to marry. If I ever remarry, I expect it to be a good marriage that lasts for many years.

It depends on what you think is the purpose of marriage. The traditional view you're questioning is that marriage is a very serious contract that is never to be broken (usually with a few exceptions, like infidelity or abuse). I suspect this view is historically an economic device for raising children: the woman raises children while the man provides for the family (please note, I'm making no normative argument for these roles). Monogamy is obviously historically useful for ensuring paternity, and there's obvious selective pressure for that norm to arise (although I've seen studies claiming that humans have always tended to practice punctuated monogamy).

These days, that view of marriage is less vital in the Western world (at least the economic part), but it still has a lot of cultural momentum. Aside from that, the only modern purpose of official marriage is legal benefits: taxes, wills, medical discretion, child custody, etc. Apart from those, I see little difference in a "marriage" and simple long-term cohabitation other than the notion that the former is a life-long commitment.