Having issues stretching text evenly

The trick is to make absolutely sure that you have the correct points active after converting the Type layer to a Shape layer.  If I drag a rectangular selection across the text below after converting it to a Shape layer, you can see that it works OK for five of the letters.

...but misses some of the points we need for the rounded letters.

You need to add those points to the selection using the Direct Selection tool (White Arrow) while holding down the shift key

That has still resuilted in some distortion of the 'O' characters

To avoid that you need to remove the points that are exactly at the mid point (height wise).  To do that select the Pen tool and add a point slightly above and below the existing points, and then remove the original points.  This should happen automatically by hovering over the shape with the Pen tool. 

@Daniel29688423zsny try using the same font as in the tutorial