Do you have a link to your app? I'm really interested in seeing web apps that work similarly to native apps, I've yet to see a great example yet.

Alas, it's still under development, several weeks away from release at best.

The biggest reason it feels native is that I'm attempting very little imitation of the iOS interface chrome. Other than a menu bar at the top and some text boxes as needed, everything is touchable graphics. It doesn't look or act anything like a web page; for instance, the click "shadow" never appears, and you can't scroll the page out of bounds (although there's a WebKit input box bug with that, too).

I'm working on a phonegap app at the moment. I definitely wouldn't say it looks native - I haven't really tried for that - but it is fast. You do have to be very careful about performance issues, but phonegap does make it exceedingly easy to incorporate native code if that is required. I would say, purely as a limited anecdote, that jquery mobile and other frameworks just weren't really fast enough for the performance I wanted to see.

Are you using any Javascript plugins at all? Regular jQuery, Zepto, Backbone, etc?

Regular jquery, jqote2, Kelvin Luck's jquery date picker, jquery autoresize plugin (though its not really working out so far) and all the phonegap javascript functionality.