A month or so ago a user named Maethius made a post about being able to tp while riding on your elk and it should come with you. Just make sure to tp a little above ground level so it wont get stuck in the ground, I'm getting all this second hand so id test it out in creative first if it was my world.
Also i don't know why but when i get far away from my elk the map shows it as being back at my base even thought if i tp back hes not there, But if i retrace my steps a bit once hes back in render range the map fixes itself.
I know this doesn't really answer your question but i hope it can help in some way with finding your elk. The new content is always a little finicky so no shame in changing game modes when it starts acting up.