Small update:

The change in the stem brought the handlebars closer to me, which made me feel "safer" and closer to my handlebars than before. That was great.

The saddle tilt that I made was also great, I wasn't slipping off.

I'm also taking into consider what ladyicon said about how I'm positioned on the saddle. I think by having been "off" for the last three months on the fit of this bike, I learned some bad habits about stretching over and leaning on the handlebars too much. I caught myself today at various points falling into the old position when it wasn't necessary anymore (I can play the piano on the bike now and I can pick up my water bottle without fearing for my life).

I'll know more after tomorrow's ride in terms of the pain on the shoulders. (And today, I rode with another friend who told me that was normal because it happens to her too -- she never thought about questioning it! I'm sure it's her fit too but her bike is easily 15+ years and her stem and headset are one piece (she can't change the angle or make it shorter).