resize and crop thumbnail photos

I created the Post Thumbnail Editor Plugin, and this sounds like the type of problem that it should work on. However, I believe that the answer depends on how the responsiveness of your site works (i.e. how does the site change the image depending on browser size — phone, tablet, etc.).

According to your example above, there should probably be at least 4 post thumbnails defined: Slider (600×400), homepage-thumb (290×180), article (600×250) and article-mobile (300×100). Using the PTE plugin you could then crop each post thumbnail as needed. However, the theme, or the plugin that manages the responsiveness of your site would need to use the two article post thumbnails in their code to refer to the different post thumbnails.