Don't be afraid to say "can't do it." Have you heard that story about how Kubrick had to have a couple highly exotic f 0.7 lenses adapted to shoot the candlelit scenes in "Barry Lyndon?" Some of the new digital cameras have pretty remarkable low-light performance, but with a 1/3" CMOS sensor, I have a hard time imagining that the HVRA1U is among them.
Noise is an inevitable side-effect of not having enough light in the scene. If the camera can't record a clean picture with the light available, add more light. Or learn to live with noise.