So I move the hive with the queen cell in it to the other side of the hive I put the queen in with the new foundation???
I do believe that is precisely what I said. Finman is right that you could move it further (in the opposite direction). You could move it any reasonable distance (but almost certainly not a mile or morefor any good effect!!).
The Padgen method, I presume, was developed to cover the situation of a row of hives, spaced such that a A/S could be done on several without interfering too much and that they were not all A/S'd on the same day! In that situation, the minimum (simplest and easiest) sensible move is from one side of the A/S part to the other.