Jessee: My 98 Patriot Ticonderoga 37' has a channel in the floor where they ran 115vac romex cables from the refrigerator area up to the console/stand behind the passenger seat. It is "very roughly about 12" from the inside wall.
One more thing. If your floor plan is anywhere near mine, if you drill through the floor you cannot get under there to put on a nut unless you can do it with the slide extended. You need to check that access and clearance first underneath. I think where you plan to drill that you will miss the fuel tank since it is between the rails. If you do decide to drill, I always start with a tiny bit (like 1/8") then put some masking tape on the bit at the depth you want. With a helper underneath, drill carefully. If you hit tin or metal I think you will know that way.
I had the same problem that you did. I solved it by purchasing a very nice leather lightweight swivel chair that swivels on a round stand that just sits of the floor wherever you place it. I slide it against the wall for more aisle space when we travel. I have used that now over 10 years and just love it. It is easy to move for cleaning and access behind it and it does not migrate on the floor or tip over ever even the roughest of roads. Best of all, the install time is ZERO.
Whatever you do, you will love the new chair. Gives you a direct view to the front TV over the driver seat in mine.
Larry Fritz