..and why would you gotta believe it would be the cause? You changed two things - the rear triangle and the cassette/wheel. It is the latter that is the relevent variable.

The rear derailleur does not know where the triangle is in relation to the frame. The factors that affect whether it moves the chain to the small cog are the outer limit screw, cable tension and friction, spring tension and the distance of the cog from the dropout face. In cases of impact damage the derailleur hanger may come into play. You need to isolate the possible causes, which is best done by releasing the shift cable completely and shifting by hand to the 2nd cog and then letting go. Logically, if the derailleur now shifts to the small cog the problem is the cable is not releasing sufficiently. If it still fails then it's limit screws or a bent hanger, assuming the chain can correctly sit on the cog when placed there.

p.s. Though obviously off, correcting the alignment would only move your rear triangle over 1 mm at most.