I like the idea of “charges”. Rather than time directly, my numbers wouldn’t change but the concept would, be 1 charge is worth up to 15 min of wildshape time. It is used when it is used, they can be chained together so no need to re-transform to stay as a bear or a cat etc…
So the transformation cost would be 4xCR, min of 1. CR1 still is worth 1hr of “charge” time to transform then using charges up after that, dependant on how long you are transformed for…
As for the DM saying different time, that is a given in any situation, the DM could have as easily said that you followed for an hour, using 4 boxes.