I use a tiling WM too (ratpoison), so I empathize. But you don't need to launch a file manager in order to drag and drop. You can open the image file in another browser tab, and then drag it between tabs. Hover over the destination tab for a moment to pop it forward.

Edit: It would be useful to make an addon that adds a contextual menu item for "Drop file here", which raises a file selection dialog and delivers the result to the drop zone. Essentially it would be the inverse of this: https://addons.mozilla.org/en-US/firefox/addon/ez-drag-n-dro... I don't currently have the time to write it.