Even with the new firmware HDMI option the FVP can be a pain.
My FVP would kill the TV ARC and the PS4 HDMI-CEC.
I powered everything off and disconnected all HDMI, then started fresh. Turn TV on turn HDMI off and then ON (I have to have it on for ARC to work with amp!)
Then connected devices except for FVP then turned HDMI on and performed search. Then connected FVP and make sure you do not do another HDMI-CEC refresh.
Now all fine but obviously no CEC function for the FVP.
Hope this may help.
(Samsung TV is not perfect either, it would remember the HDMI I used to have the FVP directly connected to until I did this as well and would switch to it when the FVP was powered even though the FVP was now connected via an AV amp.!)