You aren't doing anything with heavy streams receiving OTA TV signals, here I play with rpi
and satellite signals too, which can be way more bandwidth heavy than any OTA TV signal. eg - OTA TV raw bitrate over the air 19.3 mbps for the mux. A Satellite TV mux of 70-80 mbps is quite common.
The biggest expense your doing resource wise with the device is the playback of HD video.
On the client side (ur frontend), when using hw decoding for mpeg2, should be consuming hardly any cpu resources when playing back a video stream in comparison to sw decoding, so check that on both ends of your setups before making such changes to evaluate the differences in topology. If CPU util is extremely high when playing a simple OTA mpeg2 hdtv signal, you might need to enable hw decoding on the client.
Or is possible the program you are using to playback isn't capable of or isn't set to use the pi's hw decoding. If relying on sw decoding, I wouldn't use a rpi of any generation for the playback side of it. On a pi HD video Playback will only be reliable when using hw decoding, no matter what the source is.
For kicks I would also try flipping the existing pi hardware around. Try the pi3b+ as the server and the older pi2 as the client. Assuming that u have the mpeg decoding license for each device. Either one should be able to handle playback of mpeg2 video with little CPU util once configured for hw decoding. Which pretty much limits you to omxplayer as the video player though. Unless...
Have had some good results when using ffmpeg-mmal
remove any existing pre compiled repo provided ffmpeg first, compile ffmpeg with --mmal enabled, install that, then compile your video playback applications, tvheadend, etc from source so that they are linked to ffmpeg-mmal u just compiled / installed. That should allow hw accel options... Works pretty well for me with mpv as the player at least, and doesn't require the mpeg2 license.
I wouldn't try to use any transcoding on the tvheadend server side either, as the PI won't be very good at it, since would all be in SW.
I don't have a pi4 yet so can't comment on how well it's progressing.
They have come a long way with Intel based fanless Low Power mini-itx MBs that would be way better than a RPi performance wise,
and won't consume a ton of power. I have an older one here (AsRock J3355M based) for the wife's desktop, it's extremely quiet having no CPU fans, and if I remember correctly, draws only around 20 to 30 Watts from the wall when compiling the linux kernel. I can live with that, but can imagine they are even better nowadays.
edit: Threw wife's desktop back on the kill-a-watt, and kicked off compiling linux kernel 5.4.0-rc1
It was consuming 20-25 watts from the wall sitting idle, and 30w while compiling the kernel with 'make -j4'
When I bought the MB, I had meant to buy the AsRock Q1900M, but pulled trigger on this one instead for some reason.