Thank you all for your comments. Please, no offense is taken. It's a frustrating problem, but there are worse ones to have.
In July, due to steadily increasing activity, we roughly doubled our capacity. What we are facing today, however, is about 5 times the activity we have had previously, not just with the number of people reading but with the number that wish to participate.
The proper solution to the problem of more people wanting to participate that we can handle is to increase our ability to handle them, not to lock them out.
As a practical matter, some of the solutions in this thread are well intentioned, but won't work:
--vBulletin does a bunch of work when a new person connects that happens before determining if they are a returning registered user, so restricting the board only to registered users wouldn't make much of a difference in the load. And it would prevent registered users who do not want browser cookies set from getting in as well;
--vBulletin does not have a provision for allowing unregistered folks to post;
--The recently resolved case of Tawni Mazzone shows the efforts of folks who have been here for a short amount of time as well as ones that have been here for years. Number of posts accurately measures number of posts. Length of membership measures length of membership. Results measure dedication and effort.
The financial costs of running this site are borne by exactly 1 person - Tricia. The staff here does their best to get the most performance out of what she can afford. For about 1 cent per registered visitor per day we could afford a server about 5 times as powerful, but Tricia does not accept donations and that's her decision to make. So we tweak the settings where we can, we live with the slow response when we must, but we keep the victims first. That's what it's all about. If you want to be a part of it, it's up to us to find a way to let you. That's why I've spent this morning wringing the last bits of performance out of the server we have, and I'll continue to do it. You all keep up the good work, and welcome to all. You are the reason we are here, not an impediment or a problem.
As I am busy, I have not had a chance to triple check this message for anything insensitive, mean, or possible secret messages. So if anyone reads what I wrote and there is two ways to interpret what I said, and one of ways those hurts your feelings, I meant the other one. Back to work for me and the staff.
Thank you all.