I was looking into this some time ago for my 5th wheel but never did do anything...
I think you should be able to mount a swival TV mount in the vertical position too the inside wall close to the basement door... You should be able to place a 3/4-1 inch thick back-board in the vertical position to support the TV SWIVEL mount better...
Found these two photos on google search showing what this guy did...
The swivel mount will allow you to swing the TV SET through the open door to the outside. Then you can use the another swivel action to align the TV set to a good viewing position. When done you can quickly move the whole TV set inside the the basement area and close it up... The TV swivel action should end up with the TV SET flush against the inside wall for travel.

Google Images
I have seen some of these TV MOUNTs at LOWES and WALMART in their TV Section.
When we was using a TV SETUP in the outside Patio area we would mount a Transformer Tee at the pedestal and run one RG cable to the TV INPUT for the trailer and then run a second RG cable to throw under the trailer to run the outside TV set in the patio area...
Roy Ken