I don't think your second screen shot is an improvement over your first one.
I would do this with your first screen shot, using the Lens Correction / Manual sliders as c.frans w has suggested:
I can see a slight curve in the frame of the picture. This is caused by the distortion of your lens- unless the wood frame is warped. This distortion has to be corrected first with the <Distortioon> slider. I would highlight the numbers field by clicking on it, and then change the numbers value with the up / down arrow keys. This gives you a fine-tuned correction.
I tried it with your first screen shot and got this:
For the slider values see here:
