@utzer Well, I was correct that there is nothing in the masonry image code that randomizes the order, the array containing the images is already jumbled by the time it gets there. I'm still trying to backtrace through the code to find exactly where it is changing the order of the attachments and why but I haven't found it yet.
I downloaded your images and uploaded them to my server in the same order you indicated was correct and it put them in a different order than you got, which does seem to indicate they are being randomized.