Does the "Flip-up TV Shelf" have a power port/antenna connector near it? It should...
Where do you plan to put your power ports? Looks like the lower fronts of the shirt wards may have sufficient room. Are there drawers under the wards?
Also, what type of sidewalls does the Citation have? I searched for Thor Citation models, all look like slick-sides, so they are probably aluminum frame/foam block/fiberglass lamination. There is no wiring in these type of walls.
As 24rules suggested, drill a hole & drop a pair of wires through the floor behind the power center, and then come back up through the floor below the shirt wards. Encase the wires in split wiring sheathing:
and attach it to the underside every few feet with clamps:
Another option would be from the TV power port, if you could get to the inside of the wall from under the bathtub...
Sounds like a project to me!