D5300, Video & Consistent Exposure Issue

[sabian1982]

I do some product videos using my D5300. When i shoot the footage (1080p at 60fps) I do it with the products placed on a white backdrop which has some subtle branding on it (which looks great when the depth of field means its slightly blurred but the branding is still visible) - I've got a couple of LED lights.

I set my D5300 to manual, set the F stop to a decent balanced level and it looks great BUT when I pan left/right beyond the product in frame but more notably when I pan/zoom in and out the exposure increases or decreases ultimately resulting in quite a brightness change of the background. At times the background is completely blown out and others, really dark.

Is there any way to set the exposure at a fixed value so it doesn't increase/decrease or is there another way to over come this issue?

Would more light from an additional source to light the background work as a fix?
Would it be better off doing the product video on a green background (rather than the current white which is obviously reflective) and then use chroma key in post?