When using a traditional video camera, you focus by zooming into your subject, focusing, and then zooming out to frame your shot. My Lumix 35-100mm f2.8 appears to be capable of this, but my Olympus 14-54mm cannot. Am I correct that the 35-100 lens is holding focus when I zoom out to frame the shot? If so, would the Lumix 12-35mm f2.8 do the same?

You're referring to the "parfocal" nature of the lenses.
See is the LUmix 12-35mm parfocal? (http://www.dvxuser.com/V6/showthread.php?301967-is-the-LUmix-12-35mm-parfocal)

Do not trust any of these lenses to behave like a par-focal video zoom lens. Especially in low light situations or when you have the iris wide open for DOF. In general I have found the LUMIX zoom lenses I own to hold focus within a range of less than 4x at f5.6 or higher. Any wider f-stop and your results will depend on the lens.