Suspect you may have too strong a signal. If you have any amplification in the system dating from pre-dso try removing it.
Otherwise fit a variable signal attenuator and reduce the signal level to say around 80% when viewing a HD channel.
The FVP-5000T has tuners capable of working with low signal levels, if faced with too high a signal level they can be overloaded and the resulting distortion can create reception issues.
Note the signal level shown in my earlier post.
You should have mentioned this much earlier as it points to the likely fundamental problem.
Too much signal level since the closure of analogue creates more problems than too low a signal. The transmitter power at the closure of analogue was increased to the point where the high gain aerials and amplifiers we had to get digital TV are no longer needed.