Reverse Plank? How?

Everything has being going great until today's workout included Supine Plank Hip Dips which, excellent, I know my back and core need work. However my arms just don't go behind me, and they ~definitely~ don't go behind me when bent and supporting weight.

If I were to stand and put my arms as far back behind me as possible, we're talking two inches max from my hips, and that's an extended stretch where I'm pushing for a minute.

So help a newbie out: how do I gain flexibility when putting my arms behind me? I know the culprit is the muscles across the top of my chest, I can feel them hit a limit and stop. They mean I can't do press ups unless my arms come out to the side about 45 degrees. But I'm stumped on how to fix it. Any help would be more than appreciated!