Helmetfire - we have been mixing NVG and white light for many years in SAR, since we don't have the military imperative of covert ops we adopt what is best practise and it does work extremely well in many situations.
However, although the use of white light on the approach gives you more information, if you are looking through NVG you still need to scan for that information unless by 'moving your eyes' you mean looking under the goggles at the outside world.
This can have its benefits but usually only as a help to decide when to transfer from NVG to white light - trying to use both at the same time begs the question of what you are trying to achieve. If the picture on white light is not good enough then stay on goggles using white light to improve the illumination - if the picture on white light is good enough then transfer completely to white light. The head scan is still required to check for wires and obstacles.
Trying to assimilate the information from both under and through the goggles isn't impossible but at critical stages like landing or manoeuvering in the low hover, I would suggest that using either one or the other is best, especially for less experienced pilots.
As to winching on NVG, I have done some ad-hoc trials to the same situations (cliffs, over water, decks) both on white light and NVG and come to the conclusion that where absolute precision is required and references are available (cliffs and decks) white light gives (due to the better visual acuity) the best hover but where references are limited anyway (over water) usually NVG with the assistance of white light is the best option.
We have the luxury of 2 pilots so one can always stay on goggles for the flyaway if required - personally, after a few years of doing this job I have my goggles set so I can see my white light references on the cliff but can still 'look up' into the NVG for horizon and obstacle awareness so that I could react quicker to an engine failure instead of handing over control.
I wasn't having a pop over response times, merely asking a question - although we have specified response times the Captain would always be justified in exceeding those if more planning was required.