I'm having a very similar problem. I switched to Dish last February. I will have the receiver either get locked with the small picture in picture frame in the upper right corner of the screen, or I will lose control of the receiver with the remote being unresponsive. I've also seen that behavior when using multiview. But the common thread is that the TV Activity option will show 0 of 0 tuners in use. The only way to get control back is to do a reset on the receiver. I've also had issues with spontaneous resets. I've had the receiver replaced multiple times (I'm on my fourth receiver, three of the four have exhibited the same behavior). One possible issue is that the receiver is above 95% capacity, but the receiver is supposed to delete older programs to make room for new recordings. I had a TIVO based DirectTV receiver for about 10 years and never had frustrating problems like this.
Honu4Dish, we have had some reports sent to our Engineer Team who are looking into why the system is doing this. I can add your account to the affected list we have. Please send me a Private Message with the phone number and 4 digit security PIN. Here are -step-by-step instructions on how to send a PM https://communities.dish.com/t5/Communities-101/How-To-Send-a-Private-Message/td-p/15039