Because of a website redesign, a peer-reviewed, online-only journal no longer lists or provides access to an article I published with them. I have e-mailed the editorial board about the omission; is there anything else I should do while waiting for a response?
You should address your concerns to the publisher, not to the editorial board.
The editorial board is not in charge of the actual publication of the articles but only of their handling until acceptance. The only thing that members of the editorial board can do, is to forward your concerns to people at the publisher. (However, this may help, since the voice of the editors of the journal may have more weight…)
If the only thing that happened was a website redesign, than, presumably, all copyrights are still in place and you have to check your copyright agreements, if you can make the article available anywhere else. Depending on the copyright agreement, uploading the paper to some repository, a private homepage or a homepage at your university may or may not be allowed.