Video cameras are usually rated by their sensitivity at 2000 lux. I believe the 370 is rated f10 @ 2000 lux in NTSC, 59.94 MHz mode and f11 @ 2000 lux in PAL. While the camera gains up from there in 3 or 6db increments up to 18db (and may have an even grainier hyper-gain mode,) I never gain above 12db. The picture is just too noisy by the time you hit +18db so I don't bother even remembering about the higher settings. So what does all that techno-jargon mean in photo terms, you ask? I find that about a 400 ISO is where I'd rate the camera (using an old Minolta light meter set to 1/60.) Another way of thinking about it would be in studio terms where the DP lights the talent with 60 candles and tries to achieve an f4 iris setting. The previous example is actually for Ikegami studio cameras which have that similar f10 @ 2000 lux sensitivity. I know it's not the clearest of examples but hope this gives you a little idea of what you're dealing with.
To profile your video camera for ISO match on a light meter I shoot a standard 11 step grayscale chip chart using a waveform monitor and set exposure manually at 0 gain to get the white chip step to 90 IRE. Read the light level illuminating the chart with an incident light meter. Set the meter to match your manual exposure settings and adjust the ISO setting to match the reading. This is your base ISO rating. Do this separately for daylight and tungsten illumination. Do this again with the ND filter in to profile the change in rating.
Each 6dB of gain = 1 stop increase in ISO, or doubling of ISO speed. Most cameras clip white somewhere between 104 and 110 IRE, so this leaves a bit of highlight headroom, but I typically shoot one stop under, or double the base ISO rating for greater highlight protection in high contrast situations like bright sunny days.
You can get as sophisticated with this as you want, creating different meter profiles for different gamma settings or picture styles. With some practice you will find that this method gets more optimum exposures and DR than relying on the on camera EVF or LCD that typically can't display the DR the camera can record.
I can't say that metering will solve all your concerns. It's a little trickier than that The exposure example detailed by Razz16mm is a very good one. This is also how a vis op shades a camera in studios or in production trucks. You should refer to the built in waveform monitor of the 370 and learn what a 90ire image looks like. If you are in a controlled situation all this works but in a run-n-gun, ENG style or documentary coverage, I never have time to use meters or waveforms. In the most simplified example, beyond setting the camera to full auto, you have to learn your camera, EVF and the flip-out monitor. The main things to look for are details in the bright and dark areas. If you are loosing detail in either then the exposure is off. Make sure you've adjusted the monitor/EVF with color bars but beyond that is knowing what a proper image should look like. White hot-spots which lack all detail should be addressed with closing of the iris. If the image begins to look muddy and dark than find a happy medium by oppening up the iris. You have a stop of latitude to play with so do play. If you want a Noir look then underexpose a bit. No easy answer but much depends on your project or situation. Be sure to review your footage on a larger, well calibrated monitor as soon as you can after the shoot. I shoot with a HPX 2000, 370, AF-100 and occasionally an old Sony Betacam camcorder. These all look different through the EVF but you learn to read and adjust the problem areas and get a good average on the main subject and it becomes second nature.