I don't know your exact dimensions but I have a Direct tv system too. I put mine above the TV, in side the cabinet, slightly behind it. On my monty, there is some indented room inside the top of the TV cabinet. I used a small wire basket, hung it from the inside of the cabinet and placed the receiver in it. The space looks too small but it is not. I can see the "photo sensor" on the receiver just fine with the controller. Works great.
To get to where I could use the hand controller well, I had to shim the receiver with some pieces of plywood, painted black, then I used some long electrical tie wraps to secure the receiver to the basket.
For the basket we went to Office Depot. Got a wire letter basket and four of the stacking legs. Reversed the legs to mount to the top of the basket, wire tied them at each corner, and then used short bolts to fasted the legs to the cabinet from above.
Maybe some version of that could help you. Good luck!
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