As I have some problems getting the x11-repl with xdotool to work, I have written a little plugin, that helps with REPL interaction.
https://gitlab.com/listentolist/kakoune-replicate
https://github.com/listentolist/kakoune-replicate
Instead of xdotool it just creates a new GNU Screen session for every REPL. So the REPLs are addressed via the name of the Screen session.
Maybe this is useful for someone of you too. Feedback is very welcome!