I know this is besides the point, but why are you afraid of your screen burning out?

Because phosphor burn really happens on VFD displays.

I left "now and next" up on my Mark1 nonstop for a few weeks and now the timecode portion of the screen glows slightly more dimly than the rest of the screen.

It's very faint and you can hardly notice it unless there is a visual up with large areas of flat color such as Caledonian or Image Pan. But it is there.