Since the radio tuner is not connected to nor creates the video signals for the LCD, I'd be surprised if it was causing your problem. It's not impossible, but it's a very long shot.

The LCD is driven by RGB signals on the blue connector which are created by both the GPS and TV tuner (if fitted). The TV tuner is after the GPS in the circuit. You can unplug the GPS and the system will continue to function. This may be a useful test.

Frankly, if the problem with screen flickering has been introduced with the replacement of the screen, I would be looking at the things that changed, namely the LCD itself and its EMI screening, and the wiring that moved behind the headunit.