Okay, so I have been thinking about this and based on the preferences in the comments I have two suggestions that wouldn't disrupt the layout of the website, nor introduce any whitespace, but still represent all images more fairly and correctly and that also would give the user/image-uploader more freedom.
1. After upload there could be a possibility to choose the location and also perhaps size(within reason) of the square crop. This isn't ideal for all compositions, but it could at least avoid cropping the main subject out of the frame or slicing it in half, which at least for my tastes destroys the image. Because who wants to see half a flower? After all you wouldn't have much success selling half a car when the guy next to you has a whole nice one to sell. Seeing is believing. This would also benefit centered compositions as it would be possible to create a more in your face look for those that so desire, cropping more tightly to the subject, so one can see better at a glance if this is something interesting, yet upon opening, all of the original image could be enjoyed.
2. If this would be troublesome to program, one could instead have the option to upload a pre-made thumbnail. This would be bit more cumbersome for the user, but still okay as it would be completely optional.
What do you think,
@dave and others? Would this work?