You’re not placing your arm on the body, you’re placing your hand on the bridge and allowing your arm to simply touch the body where it touches. Most of the time, this means you’ll have a forearm anchor against the upper part of the body. The amount of your arm that touches the body in between is, as you point out, determined by the height of the bridge. Since the bridge is higher than the body on every guitar, there will always be a little air gap in between. That’s fine! Leave the air gap. It may be a little larger on a Les Paul, but it’s always there to some extent, so there’s nothing wrong with the Les Paul in that regard. Here’s what this looks like on the Les Paul:
I think we talk about the air gap a little in the “Intro to Picking Motion” talk, and leaving it there intentionally. Of course, since you’re sitting on the bridge, you have your muting too. So that part is for the most part, automatic. Let us know if this helps.