Does watching live on a client stream through the server? Wondering if there's a problem with the server's ability to deal with the bandwidth when recording from the HDHomeRun, but if playing live via a client does the same, then that's a non-issue.
If MC tuners are set up correctly, connected to the server only, then yes, the server controls the stream from the HDHomeRun and streams it to the Client. If you have Time Shifting on, MC will still be saving JTV Time Shift files on the server, even though you are watching on the Client.
Reading your description of the problem (choppy, digital noise, jumps around, etc), it really does sound like a poor signal problem. The HDHomeRun software may do something special to handle that situation, and hence show a better picture. As you report that Live TV plays fine on a Client, that creates some doubt in my mind, but that could be a timing coincidence. Or Live TV on a MC Client does the same thing that the HDHomeRun software does to remove the problem, like dropping incomplete frames.
Does the HDHomeRUn software allow recording and then playback, and if so, does the recording show the problem?
If you watch TV on the MC Client without recording, but Time Shift the program a small amount, does the problem re-appear?
Regardless, I never see less than 100% Signal Quality and Strength since I replaced my antenna. I had a TV Antenna company install it for me, as they have the equipment to test the signal strength and in my case, point it at the strongest signal source, and add a high quality splitter for the three outlets I have. You should note that sometimes a signal that is too strong is just as bad as a signal that isn't strong enough, in which case an installer will use an In Line Attenuator. Did you use a TV Antenna company, or just buy a new antenna and replace it yourself?
Of course there could be other PC hardware, network bandwidth or reliability issues, but I would go back to the signal quality/strength from the antenna and see if it is doing its job properly.
PS: Enjoy the game live. Also, what version of MC are you using?