In Vim, you can move a window to an edge of the viewport with H/J/K/L. Vim will make sure the window occupies the whole edge and resize/shift the other windows around it. Is there something similar for tmux? move-pane doesn't seem to have an option to preserve sizes like Vim does for you. rotate-pane is not the same behavior either and does not guarantee the pane will find the correct edge.
I can think a couple of ways of achieving this, but I don't think they are exactly what you are after:
(ctrl+b) = the default trigger/shortcut.
One option is to use (ctrl+b) + { for moving left, or (ctrl+b) + } for moving right, this moves the content from one pane to another, while using (ctrl+b) + space to rearrange the panes in different layouts.
You could use select-layout to "shortcut" the wanted layout if you don't want to browse through all of them, for example (ctrl+b) + (alt+#) where # is a number between 1 and 5. You could also zoom in a pane with (ctrl+b) + z maybe to help.
I don't think you have a simple shortcut option to "move the pane around the window and resize the remaining panes accordingly" if that's exactly what you are looking for.
