Thanks for the suggestion! At the risk of looking like I've asked for suggestions only to shoot them all down, I didn't want it to be as prominent as that and I worry that because of the moment arm, plugging something into the cigarette lighter side would stress the screws (I'd have to be too careful when using it, if you know what I mean).
I think I'm to going to look closer at mounting it under the arm rest after all. Maybe charging cables wouldn't be so obtrusive or I could just take off the pad when I needed to and if the Velcro gets worn out or comes off, I can just replace it. Seems simple and obvious, but I guess maybe I was looking for the perfect solution that I hadn't considered. (And then, maybe I've been given the perfect solution and I've discounted it!)
When I finally put it all together, I'll post the final result.