Did you actually disconnect all other MoCA devices and did you use a new piece of RG6 to connect the Hopper to the hub at the dish, just as a test?
Also, I would try "un-networking" the Hopper and "re-network" it using Ethernet to get wireless out of the picture.
Is OTA in the picture when these reboots happen, as in, watching a recording made from an OTA broadcast? (you said no OTA, but does that mean now or always?)
My very occasional reboots have been, as others have posted, related to the AirTV dual OTA adapter and the signal strength, it seems. The other day I had to disconnect my antenna briefly, and the loss of signal to the OTA seemed to cause a reboot. The other cause of reboots that I've seen are when trying to, very slowly, transfer recordings from my old leased Hopper to its replacement, a purchased one.
Are you all finished with transferring recordings?