I'm 6'1'' and ride a 56cm.
From my noob eyes it looks like your torso isn't bending much but your arms are reaching out... that's probably giving you the feeling of feeling stretched out. Rather than following general fitting advice from online resources try to find someone who is an experienced fitter.
I felt OK on my 58 and felt my 56 was too small so I got a setback which created more issues. Got fitted and found out I needed a 0 setback and some adjustments before the fit was PERFECT. I probably belong on a 57 though.
In your case I would say don't get a 56. The drop from the saddle to bars is going to be more. I know it sounds counter intuitive but try to raise your seatpost a bit and move your seat back. Take up Yoga if you have to.
As a 6'1'' male this is what I have to do to fit on a 56. Notice the drop...