I certainly understand your frustration, especially given how much you have invested into the project.
Yes, I’m sure that with enough investment of time and money, we could work together to make my plugin solve your problem. But I wouldn’t call that a “wise investment” from your point of view.
Bottom line: in my opinion, a WordPress Network (“Multisite”) of two Sites is the cleanest solution to your problem. Each site would have only one Theme, eliminating any usage of my plugin, and avoiding all of the problems that my plugin faces revolving around the fact that WordPress is internally built with the assumption that only one Theme is being used for a Site. To make my plugin work properly with all Theme options, I would have to intervene during the setting of each option (Widget, Menu, etc.) and store data in the plugin for each option of each Theme, then intervene as each Theme requests information about its options during the display of each page of the site. Not all options are handled in the same manner by the WordPress Core because the design assumed just one Theme, not many, in use.
Integrating two WordPress Sites to work together as one web site takes some work, such as creating unified Menus that cover both sites. From a programming perspective, viewing data from one site on another site is made a hundred times simpler when they are in the same WordPress Network by the fact that they share the same database, and there are functions available that let you temporarily change site, get the data you need from the other site, and change the site back.