I submitted a support request earlier, and wonder of wonders, they got back to me pretty quickly! The way to get the dialogue box for switching back to show up is a bit ridiculous, but it works, which is the important part.
Here's what they told me:
Thank you for your inquiry. Yes, a redesign of the entire LiveJournal site was released today. A pop-up was supposed to appear for all users when they visited the homepage, but apparently that has not displayed for all users.
You can view this pop-up, which contains a link to switch back to the old version, by doing the following. I apologize that the steps are a bit unwieldy; an icon is not displaying properly at the moment.
When viewing any system page that shows the standard blue header banner (such as the home page), there will be a link labeled 'Post in blog' near the right side of the banner.
To the right of the 'Post in blog' link, there is what appears to be a blank space, and then an envelope icon. Click on that blank space between 'Post in blog' and the envelope icon'. The image at
http://ic.pics.livejournal.com/markf/1314111/43922/43922_original.jpg shows how this will appear.
A dialog box will appear with information about the redesign -- at the bottom of that dialog, there is a 'Switch back to old version' link you can use to return to the previous version. An image of this dialog box can be seen at
http://ic.pics.livejournal.com/markf/1314111/44151/44151_original.jpg.
Also, if you're getting Frank nibbling on the wires instead of entry pages, once again, ?style=mine might fix things. It seems to for me.