Cable channel change delays beyond whatever delay is built into the cable box are typically at rez changes. Not always the ideal thing from a deinterlacing and scaling thing but you can usually reduce the delay by setting the cable box to 1080i, or 1080P.
I have a very different setup, my TV never sees anything but 1080P as I have an outboard Video Processor that does all the switching, scaling and deinterlacing and I am using an HP X280n Windows Media Center extender paired to Ceton Cable Card equipped PC for cable TV. I never have synch issues with the VP. I use only one HDMI port on the TV and the Video Processor has 8 I think.
Mits WD-92840 92" DLP - Lumagen Radiance XS, Martin Logan Motion 40s, Ascend Sierra 2s
Older 58" Panny Plasma -DVDO DUO, JBL Studio 530
Pioneer AJs, PSB Images, Usher S520, JBL HLS-610, Definitive SM45, MusicHall Marimba