There's really no excuse for not testing in all browsers but I can understand the impulse to "get the change out the door" too.

For myself I tend to iplement a change in a separate file and leave the old page in place. Then as I test each browser I use the browser ID to redirect people to the changed page as I test their browser. Then when I'm done I replace the old page and remove the redirect.

It sounds strange but I've found it's a good way to get changes out as soon as possible while not risking what happen to the author here.