If your tutorial works then the tutorial is fine.
I looked at the description. For r2 parity you can use this:
https://www.speedsolving.com/forum/threads/big-cube-bld-discussion.16775/page-24#post-1057684
When I was learning 5bld there was only few sources so I figure out the way of doing +centers with easy comms. They are faster and simpler.
I'm not sure how I did +centers on D layer with U2 method but i think it was like (with buffer on Ub):
- setting center of D layer to Df (Im not sure how to describe it)
- setup m d2 m', next U2, next m d2 m'
- undo setting center on D.
- next target.
If the targets are on U and D layer I was just putting D pieces under the pieces on U layer. I mean if my target was Ur I did y rotation, than setting it to Dr (after y rotation it was Df) and next easy comm: m d2 m' U m d2 m' U'.
For special case with targets on U layer and on side layers (B, R, F, L) I think I used same alg, though it's much simpler to use comm like setup U, next m d' m' U m d m' U', undo setup U'. Thats only idea. If you feel comfortable with your method, it's fine. But I remember I was using it when I started 5bld. It saves a lot of doing and thinking.