I have a .NET application in which most of the UI is custom. On some of the pages, I am using ExtJS4 components, such as Grid, to display a table of Users for example. I a
I had to create an application that included several pages that were not ExtJS components. For me it was about 50/50 so a little more ExtJS than yours. Multiple instances of Ext.Application was not workable when I tried because of how the viewport was tied to it.
I ended up using one Ext.Application with a single viewport (which is nice for resize management), I created a "proxy" Ext.panel.Panel view for the other (non-ExtJS) pages and I dumped the content of the page into this panel's html config when it was rendered using a servlet - I did not want to use IFrames but I suppose that could be another option.
This worked out nicely for me and I was able to take advantage of the MVC achitecture like this.