First of all, I do really feel your pain. And am sorry to hear that you have lost your menu/widget settings. I tried to caution in the FAQ about possible, but to me unknown, dangers of the Workarounds offered, i.e. – “Note: this approach only allows Menus to be set for one Theme. Using this method to assign one or more menus to a Theme will unassign menus for all other Themes.” Yours is the first report I’ve received from someone trying to set both widgets and menus on each of several themes.
Unfortunately, I do not know of an answer to your question “how do I have multiple themes, each with their own menus and widgets, on the same WordPress site?” I did not consider this situation when I originally designed the plugin. More recently, when I did start to get questions on the subject, I discovered that WordPress was not designed with any thought given to multiple themes, because Menus and Widgets, among other Theme options, (1) assume that there is only one Theme, and (2) do not store their settings in the same manner. Which is why the FAQ says “We hope to build this functionality into the jonradio Multiple Themes plugin in a future Version, but it is not clear just how practical that is, so the best that can be said is: Maybe.”
Until and if I am able to create a future version of this plugin that will itself support separate sets of widgets and menus for multiple themes, I cannot recommend this plugin for your situation. The only solution that comes to mind is having multiple WordPress sites, either as separate installations, or using a single installation with the Network facility, all on the same domain name, either as separate folders or subdomains. Each WordPress site would then have only one Theme, and you would not need my plugin at all.
Again, I do sincerely apologize for the work you have lost. I will update the FAQ to more specifically outline your specific situation to save others from suffering the same anguish.
If you have any other questions, I will be happy to address them. Given your experience with my plugin in your specific situation, I would strongly suggest that, if you want to try any other approach to solving your problem, you should build a test WordPress site, and test there first before risking losses on your “live” site like you’ve just experienced.