Kitty has been my daily driver for quite some time now, I really like it for its rich feature set and extensive configuration.
You can use its goto_tab
action with 0 and negative values to get MRU behaviour.
See more here: https://sw.kovidgoyal.net/kitty/actions/#action-goto_tab
Just tested* and it doesn't seem to work, no. I don't know if it's doable though, it may be.