You can do that using WP. Sorry if I take advantage of your question and I promote the plugin I uploaded in WordPress few days ago. With Freesoul Switch Theme you could assign a different theme to each page. I’ve created this plugin for debug purpose, but in your case you could use it to permanently assign a different theme for each page. The actual version of my plugin supports only the front end. It means that if you want to change the theme options … it would not be a good fit with your case. It could be a good fit if you use only one parent theme and you build a child theme for each navigation style …. In that case you would have the same theme options and you could manage the differences in the css and php of the child themes. I suggest you also to look for other plugins, maybe you will find a plugin similar to mine that allows you to change theme options without switching every time the theme in the back-end.
If at the end you use my plugin I will be very happy to have feedbacks, especially regarding the weak points that I could improve, because due to the fact it’s public since few days, nobody has used it until now.
Another option could be to build a multisite, in that case you could have 3 dashboards that are always accessible and you could assign a different theme for each single site. To learn more about multisites read here: https://codex.www.ads-software.com/Create_A_Network?
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