Don't bother recreating the app with any native features unless you really need to. Having said that, I have also found that PhoneGap is extremely buggy with jQuery Mobile and nested lists (the back button didn't actually work, like it wasn't keeping a history). No guarantees it wasn't my/the other developer's fault (some other developer gave me the JQuery Mobile code) and I also can't say if it is a bug in JQuery Mobile or PhoneGap or if it extended past nested lists. I just rewrote the app using a native ObjC.
I'd personally just go with a native ObjC app that has one WebView pointing to your website and some sort of mechanism for detecting if the internet is offline and displaying a message. Or use the caching manifest on your site.
I'd personally just go with a native ObjC app that has one WebView pointing to your website and some sort of mechanism for detecting if the internet is offline and displaying a message. Or use the caching manifest on your site.