I think it will be too confusing to move different forms into different websites/projects as logically they are all the same "application" and the screens interact in varying degrees.
You have a point but I believe that, if you spend some time splitting both projects like that, you'll have much less trouble in the future upgrading and maintaining the tools. We from Ext.NET simply can't foresee what wrong may happen with such a mix up. Specially if you use both frameworks in a same web page!
If you are not using both resourceManagers in a same page, then you are not effectively "sharing the memory and data structure" between the two versions but transmitting data between them thru page requests. In this case, having both libraries in different projects (in same website) should be straightforward -- and much easier to maintain, as pages will be able to have the same namespacing and all, without conflict, no need to rebuild 3rd party libraries, and so on.
You will probably have a same business logic in your application, which can be made into a 3rd project (common between the two others), and used as a class library. I'm just sharing my thoughts about your scenario as maybe it may help in some way. A second opinion. Maybe worth a try.