May I ask how long you’ve had the Tablo for and whether there ever was a time you had good reception on the Tablo? From what you report, seems you have a reasonable reception.for other devices and I’m wondering what convinced you to try for so long to make the Tablo work?
I’m wondering if you have an electronics retailer like Best Buy in your area? I don’t like to suggest these types of behavior, but oftentimes it’s the only recourse. Go get a device from them (or from Amazon or Newegg) and if it doesn’t work, then you can return it. That’s how I got my Tablo. If I had poor channel reception out of the box, there wouldn’t be a Tablo in my house, since I’d assume it wasn’t working for me.
Did Tablo Tech support look at logs, etc. on the Tablo to determine that “it was your problem” to paraphrase? Again, that seem to have been the appropriate time to return the Table to the point of sale unless Tablo support offered additional steps you could take to improve performance.
Just detail for me the steps you perform to do side-by-side testing. For me, it want’ an easy device to do a true side-by-side comparison of my native TV reception vs over-Tablo reception (My wife balked at helping me carry a 65-inc TV upstairs to the room where I keep the electronics :O) so the final steps were a leap of faith that fortunately turned out well.
I’ve heard that longer coaxial runs cause signal loss and signal interference, hence the need for amplifiers and splitters (again, I’m lucky in that my setup works perfectly with a flat antenna stuck in a window - bought from Amazon, ofc)
I do notice differences when that antenna’s amplifier is on or off.
From the antenna, I have my Tablo hardwired via Ethernet into the router, and then it’s wireless to the one viewing room and over Ethernet to the other room. I’ve also, before going the Tablo route upgraded my WiFi and I’ve measured that I can nominally get in excess of 30Mbps throughput at the Roku or the TV that runs the Tablo app - I an shocked that very strong 802.11ac signals over relatively short distances are about 40-50Mbps slower than a native Ethernet, but I’ve learned to live with it. My next project is to get Ethernet to the 2nd viewing room. 
Sorry if all of this seem long-winded and pointless, I’m just trying to see if there in your setup are areas where the Tablo workflow could be interrupted. Can you for instance screenshot the mobile setup app channel list?
In the end though, if you think it’s a “Just that one Tablo” I’d see if the fine folks at Tablo won’t offer you a trade-in or a goo deal on a refurb. If you think it’s endemic to Tablo (and here, hopefully if you provide your zip code. other local Tablo users can chime in with their experiences) then you should move off Tablo. Tivo, HDHomerun, Sling, YouTubeTV are all alternatives that may be a little more satisfying, Even Plex has some offerings.