One suggestion.... Make it faster to skip back and set the start date, or allow manual entry. I'm not even that old but it's a lot of months to click backwards on Android.
I just pushed an update to only update the grid of weeks once the date picker is unfocused (onblur event) rather than recomputing unnecessarily on every change event. I suspect that is what caused the bug you're describing, but let me know if it's still broken.
(I didn't know the browser had a native date picker.)
And yep, the browser date picker (https://developer.mozilla.org/en-US/docs/Web/HTML/Element/in...) is a major time saver. This project uses the native color picker, too.