What you describe is called a “masonry layout” for WooCommerce shop. This is an interesting idea and I will certainly see what can I do about it for future theme updates. Problem here might be that WooCommerce actually also display products using shortcodes and the masonry layout would need to apply for them too, most likely.
Actually, I think there might be one other solution. The theme is fully compatible with Beaver Themer plugin which you can use to create any layout for your shop page. The plugin is paid and if you decide to try it, I would suggest asking its support whether the masonry shop layout can be built. I think it might be possible, but I’m not the plugin author ;)
I’ve just released a new Monument Valley theme version 1.5.0 that contains a masonry shop layout out of the box. Just make sure you set “Uncropped” product images in Appearance → Customize → WooCommerce. The update also fixes issues you have reported :)