I have no idea what’s going on there.
I opened Firebug in Firefox, and there are quite a few things happening in the background after the page is loaded… some ajax stuff happening, Google Maps, lots of content from Cloudflare, etc…
I did a test signup, and although the resulting page is blank, I can see with the developer tools that all the POST fields had been set correctly.
The rewrite.php is in the includes folder for WordPress, in the url_to_postid function, and it is somehow getting called while the global $wp_rewrite object has not been created yet, because that is what is being referenced in line 449 that you mentioned in your error.
Perhaps some of the posted fields from my plugin, or the query variables in the URL, are confusing one of the other plugins? It’s totally crapping out before WordPress headers are sent, so that’s about the only thing I can think of. The function in my plugin that processes the signup form is attached to the WordPress wp_loaded action hook, but doesn’t create any output of its own (stores results in a class variable which are then displayed when the shortcode function is called… but, we aren’t making it that far).
At this point, you probably need to do a process of elimination, turning off a bunch of those other plugins that are loading all the extra stuff on that page… or, turning off all plugins except mine, and then turning them on one at a time and testing again until the problem happens again… at which point you will know what is conflicting, and then I could try installing the same plugin on my system to see if I could recreate the issue and have access to error logs and such.
Also, you say it worked before on the same server, but has it worked at all on this particular site yet? If so, what changed since it was working? If it hasn’t worked on this particular site, then we definitely need to figure out what the conflict is… most likely a plugin or theme.