Horrible night-time video noise from the NEX-5n - need faster lens ? Other solution ?

Hi

Part of my usage of the NEX-5n is shooting video at night, sometimes from a car. I have the 18-55mm kit lens and a Sigma 30mm lens. I find out that the movies have excessive noise at ISO3200, and the minimum acceptable ISO for no-noise is ISO400. ISO800 is so-so. But at ISO400 the images are very dark, and even at ISO800.

Also, the focusing is not good, it sometimes loses focus and hunts for focusing.

I would have liked an option for noise reduction in video. There are the "High-iso noise reduction and long-exposure noise reduction" settings, but they don't do much.

Is there any solution to improve the video noise at night ? Is there any post-processing software that could help (and is affordable) ?

My old Panasonic LX3 did quite a bit better in night-time video (maybe because of the F2.0 lens ?), and even my Point-and-Shoot Canon EPLH 300HS seems to do better.

I am frustrated.

Thanks !