iOS 6 breaks GeoLocation web app

Question

We have an HTML5 app that uses web sql, offline functionalitiy and the geolocation API with the enableHighAccuracy option set true.

Since iOS6 position.coords.accuracy often reports high values (100m+) even after a couple minutes warm up outdoors whereas iOS5 went to and stayed at 5m accuracy fairly quickly the same on iPhone 4S, iPad 3.

One workaround is to kill all apps then run the Apple map app, press the current location button and then start the HTML5 web app in which case things work as expected.

Thanks to SO12503815 we are not running mobile-web-app-capable.

Any workarounds, aside from coding a native app ?