I am fairly sure these "transitional flickers" are caused by the TiVo, not the TV.
My TV is set to Native. I am using HDMI.
During the transition to a channel with a different format , I can see program information for the channel I am changing to. The program information's size and location is changed, but it is still readable if you can read fast. In this distorted information panel I see the current format in the distorted information panel, and then the screen goes black, then I get the channel I switched to. When I press the info button, I see the correct format in the information panel.
What seems to be happening is this; I am watching 1080i, I switch to a 480i channel. The TiVo sends the 480i channel to the TV with a switch indicating it is 1080i. The TV chokes on this. The TiVo then sends the 480i channel with the switch indicating it is 480i. The TV is now happy.
So for that brief moment, TiVo is sending the wrong format switch, screwing up the TV.