Yeah, it's kind of a tight fit... NOT desirable in this case, LOL.
I used a few pieces of electrical tape as a temporary measure. (Not the best/safest idea, but as you mentioned the keyboard is already raised a bit, and there isn't much room to raise it any higher.) When I get around to actually using the thing, I've been thinking I may try either filing down the header a bit and connecting an extension cable, or simply desoldering the header completely and soldering an extension cable directly to the board. Then it's out of the way, and usable.