Setting Featured Images to Be Squares

On my website's home page and category pages, for older posts (before we made square images to be set as the "featured" image), the grid gets all messed up due to featured images being different shapes / sizes... is there a way to set a default "square" image to be used when posts have no image... and is there a way to force posts with images that aren't square to be cropped to be squares (only the featured images for purpose of the grid)?

Here's an example of a page where the grid gets messed up due to no featured images or different sized images:

and you can see what the grid should look like on the home page:

I have granted support access via the wpmu plugin, in case that helps.

Thanks for your help!