You can try a Logitech Harmony remote. You'll want to use an ir to rf remote like the Harmony Ultimate.

How about facing up behind the tv. Temp mount and try remote.

The receiver eye for the remote signals is on the front, so if it's not facing you it MAY have trouble receiving remote signals.

As far as 'interaction with the TV' all it needs is a cable from one to the other, so it may have to be longer, but other than that you can put it anywhere.

Will the hearth stick out into the room so there are side walls on it? If so you could hang it vertically on the side wall, so the front of the unit faces the room. Not invisible but out of the way.

You can place the box just about anywhere. As long as you have power there and can get the incoming cable to the spot and a return wire to your options are pretty wide open.

You will need an infrared repeater system to carry the remote command to the hidden location.

Here is a link that might be useful: IR repeater system