Etymotic HF-2s (or similar) noise-blocking earbud headphones. People know that they'll be distracting you when talking, and they reduce the outside noise quite a bit.
As for the perception issue, that's more of a showmanship issue. For people who aren't in your field but do judge, I find a few stereotypes work out well. At my last job, I filled unused screen space with random API references. The busier and more technical my screen looked, the busier and more technical I looked as a result. It's the game you have to play when people don't let good work speak for itself.
I definitely had the screen set up as you described, but I still found working with constant open-back visibility to be pretty terrible.
As humans, though we share this with most animals, we have a strong desire to do important things (eating, defecating, sex, spiritual journeys) with at least some degree of privacy. Work, at least of the mentally taxing kind, falls square into that category.
As for the perception issue, that's more of a showmanship issue. For people who aren't in your field but do judge, I find a few stereotypes work out well. At my last job, I filled unused screen space with random API references. The busier and more technical my screen looked, the busier and more technical I looked as a result. It's the game you have to play when people don't let good work speak for itself.