Maybe the OP can clear it up, but I'm pretty sure in this case he was talking about the stutter you can get from using very high shutter speed, not related to the grid. You'd even get this shooting outside. I shoot a lot at 1/50th (or 1/48th with magic lantern) and 24p and don't have trouble at all with tungsten or other constant light sources.
Yes my problem was specifically related to the faster than 1/60 shutter speed and not the lights. I upped the shutter speed to deal with the fact that my scene was a little too bright. I forget what I used, but it was in the 1/200 range and as long as the subject was still, it was ok, but any side to side movement, and oh man, awful.
The light kit I rent is an ARRI tungsten constant light source.
I've decided to buy the light kit and solve this from the light side. I was not happy with the ND filter color cast and while I may get a less drastic ND filter, I'm going to move to a softbox and scrims and maybe a dimmer or two to get control over the lights.
I'd like to stay under ISO 400 with a 1/60 shutter speed (or 1/50 for 24p) and in the 2.8 to 4 aperture range. But I think attacking this from the light side is going to be the way to go.