I’ve never tried to cast to the fvp4000t before now; however on the latest software 1.01.49, my experience casting from windows 10:
HD works for about 5 secs.
SD works, no problem with video, but no sound.
some of the older kindles have mini hdmi and my experience connected directly via hdmi cable, demand 5 (online Channel5) couldn’t get through the compulsory adverts. The advert contained some sort of pop up to click on to access the advertised product and this would crash the app. 4OD – recognised kindle was plugged into external display and refused to work except on device display. Presumably worried about being able to copy off hdmi output.
I assume you don’t want to stream netfix as that’s already on the fvp4000t, which leaves amazon tv. The fire stick ~£25 plugs into the tv and I’d imagine it’d do what you’re looking for.
The fvp4000t will play back HD from NAS etc., but casting to it I would imagine will always be hit and miss