SureAI

After killing each assassin, they turn ethereal for a few seconds, then come back to life. They do not teleport away as the wiki says they should. I managed to grab the amulet from the dead body, ran off, and completed the quest without permanently killing the assassins.

My save-game is now permanently stuck playing the special battle-music from this fight. I was able to temporarily stop the battle music with the "removemusic" console command, but it starts right up again every time I load my game. Most likely because scripts are still running from this quest due to the teleportation bug.

It is annoying enough that I don't think I can continue playing the game while keeping my sanity. Is there any way to fix my save?

Welcome to the forum !

Can you try to load a previous game and try again?

Starting a new fight helps in Enderal too.

You could also upload the savegame.
It's located in ...\Documents\My Games\Enderal\Saves, we'll need the skse and the ess of a manual (no quick- or auto-) save
pack them to a rar or zip archive and attach them to a post here

Reloading the save, and restarting the game doesn't fix the problem. I've gotten in to multiple fights, and completed other small quests without any effect.

I've attached my latest save files as requested.

Thank you! The bug is known and we are currently looking for a solution.

Is there a chance when a solution is found, that it WON'T be able to repair my existing save game? I don't want to keep investing time in a save file that isn't fixable.

Also, I just want to say "Thank you" to everyone involved in this mod. The level of quality, and support you are able to provide for a free mod, blows my mind. Keep up the great work!

Yes, that can happen. If the error is stored in the save. Sometimes saving then reloading (but not always) helps.
You can theoretically repair a save (but you have to know it well).
In this respect, frequent manual saving is recommended.