Have any of you contacted Tech Support?

Two things come to mind as potential causes of such weirdness: dust and oxidation. We don't think of HD receivers in the same way we think of computers, but they are. Instead of having lots of wired components and circuit boards rigidly fixed together, as in the old days, they are made up of circuit boards plugged into various types of connecting blocks.

A 1070 isn't a computer and doesn't have a cooling fan to fill the case with dust. But heat from components causes convection, which pulls dust in along with cool air. Dust can short things out and cause all kinds of mischief. It is easily removed with a can of compressed air or an appropriately grounded vacuum.

A long time ago I learned that when a computer didn't quite work right there were two things to do before calling the repair guy. Reboot it, and if that didn't work, reseat things like the sound card, video card, modem, etc. You've all mentioned rebooting. But no one has said anything about reseating the circuit boards. They get oxidation in the connectors. Circuit boards can be loosened due to vibration or heat-induced expansion and contraction. I'm sure the Outlaws would prefer that you not mess with the circuit boards if your 1070 is still in warranty, but if it's not, have you tried reseating them?