Tvheadend

I can tell you a cheat that will probably work if all else fails. Install the latest version of Mythbuntu, then install TVHeadEnd on top of that, then disable the Myth stuff from auto-starting at reboot. In my testing, TVHeadEnd will then find and use the HDHomeRun(s), and it's a heck of a lot less hassle to configure than the MythTV backend. I haven't installed this permanently yet (still waiting for them to fix the "bad skip issue" in the TVHeadEnd addon for Kodi, see http://github.com/kodi-pvr/pvr.hts/issues/92 ) so can't answer questions about it, but I did try it on an older machine long enough to confirm that it will work.

I'm assuming you've already tried the steps on the page at http://tvheadend.org/boards/4/topics/10322 (particularly the part under "Install HDHomeRun Add-Ons"), which were apparently written for use with an older version of Ubuntu and have not been updated since? I know it says that won't work under Ubuntu 12.04 but maybe installing the HDHomeRun drivers would be enough to get it working in 14.04, I have no idea. If you try it, please let us know your results, because I'd be curious to know if that will work.

I can confirm it works with 14.04 and hdhomerun. just be sure use tvheadend 4.05 or higher version, 3.9 is not working to me.

I can also confirm it works with 14.04. I am specifically using the HDHomeRun Prime for Over The Air transmissions. It might help to install the hdhomerun gui on the same computer that is running tvheadend to confirm that the gui can see the tuners. It also might help to make sure you're using the latest firmware (https://www.silicondust.com/support/downloads/). I know that I did not have to install the add-ons listed in K Shea's link for 14.04.

I know you were working on this a month ago, but did you get it worked out or give up?

I updated to tvheadend 4.05 and it picked up the hdhomerun tuners for me, all is working.