I'm an idiot, but I don't have the manual on hand right now. Is it possible to stop the record light from blinking, either by making it a solid light, or by turning it off completely? Actors seem to find it very distracting. Thanks.

Toggle the Tally Lamps on or off via the setting in the Camera System menu (as described at the bottom of page 83 in the owner's manual when you have it in hand).