However, in a recent project at my day job, I think I'm getting pretty close to a slick and seamless mobile web app experience that closely emulates a native one. See the work in progress at: https://staging.ctmc.org. Keep in mind, this is not the final product yet. I will update this post with a new link when it's fully baked.
One of the main downsides to this project in terms of speed is that the site is fully responsive. While this is generally seen as a feature (and I would argue that it is in many respects) one major issue is that more resources are loaded to the mobile device than necessary. Even though it uses a "mobile first" approach in terms of CSS, there are other resources that are present on the page (larger images for the banners, some scripts that don't get utilized on mobile, etc) that play into a longer than necessary page load time.
I borrowed several UX elements from different native mobile apps.
1) The slide-up footer menu, for example, mimics the one found in the Android Google+ app. By hiding that menu onTouchStart of the body, and re-introducing it to the page via the sliding animation, I have greatly decreased the common problem with fixed position elements on different mobile environments.
Or if you think it's fantastic, I'd love to hear that too :-). Thanks for taking the time to read this!