I don't know about free programs for gif making, just one which as far as I know is a one off payment for a program where you can make gifs. Maybe try websites like
gifmaker? But not sure if they'll let you crop. Don't think that one does but I imagine there are others which do.
I attempted some things from those gifs. Sorry terrible quality for the last one to keep the filesize small enough to work on
For that last one I could attempt a top & bottom animation to make the quality improve? So at the top you'd see her circling, & the bottom you'd see him. I don't know how it'd look but the quality should improve as there will be less frames in the animation then.