I did a couple of quick measures on my iPad. I run 100 successive cv::pyrDown and measured the time in milliseconds. May not be the most accurate but it gives us an idea of the results.
I cannot compare directly both implementations because with the images supported by both implementations, the modified code will not run.

I tried to evaluate the speed on similar-size images.
Current implementation:
520x520, 1 channel image: 306 ms
521x527, 1 channel image: 356 ms

New implementation (is crashing on current implementation):
521x521, 1 channel image: 333 ms

The new implementation is close to the current implementation for images of similar sizes. It makes me think the alignment code is behaving properly or at least doesn't drain performance much.
Let me know if you have other tests in mind.