Ring expansion in cyclic compounds
You overlooked the strain from the sp2 carbon in a small ring. The ring strain you have listed is based on sp3 carbon. sp2 supposed to have a planar triangular geometry (120°, compared to 109° for sp3) and will be more strained in a 3 or 4 membered ring. 6 membered ring will be best followed by 5 membered ring.

Also, you have discussed a lot about the stability of carboncations. Acid catalyzed elimination/rearrangement reaction is a thermodynamic condition. The stability of product is more important than the stability of intermediate.