If I remember correctly, your inverter is directly under your bedroom. It would not take much to install a box in the bedroom and run a short length of 14/2 w-ground down to the inverter with a male plug on the end. You could run it up the washer drain chase. Just a suggestion to keep the bugs out.
My unit had 2 12v utility outlets. One in the bedroom and one outside just below the bedroom window where the exterior Thule mount and coax connector for outdoor TV use was located. You also have a 12V junction/fuse panel in the front garage which is also under you bedroom and easily accessible.
BTW, you explained just fine the first time just didn't know you don't have the 12v Jensen bedroom TV.
Edit: If you want to go low $ you could just run your extension cord up the washer drain chase and leave it there.
The recipe for perpetual ignorance is:
Be satisfied with your opinions
and content with your knowledge.