A couple of people have reported similar issues, most likely caused by information in the game cache folder being carried over into a new game. Deleting the files in the '..\Documents\Larian Studios\Divinity Original Sin Enhanced Edition\LevelCache' folder before starting a new game would prevent that, though it shouldn't be necessary.
Please email your most recent save before entering the Black Cove to email@example.com (or a Dropbox or Google drive link, etc).
Each save is a folder in the '..\Documents\Larian Studios\Divinity Original Sin Enhanced Edition\PlayerProfiles\<ProfileName>\Savegames_patch' folder.
In Windows Explorer you can zip a file or folder by right clicking on it/them and selecting 'Send To | Compressed (zipped) Folder'.
Alternately, I will describe how you should be able to fix the problem, by extracting the contents of the save before entering the Black Cove, and removing the associated level file, as well as any for any other areas you have not been to yet, if applicable.
First, extract a pre Black Cove save using the 'EE pak extractor':http://larian.com/forums/ubbthreads.php?ubb=showflat&Number=572322&an=https://s3.eu-central-1.amazonaws.com/nb-stor/dos/ExportTool/ExportTool-latest.zip
After starting the program, switch to the 'PAK / LSV Tools' tab, in the 'Package path' browse to the Before-Black-Cove.lsv file, then for the 'Extraction / source path' browse to that or another profile's savegames_patch folder and enter a new folder for the extracted files (you can copy/paste the path from the path listed above and edit it; ie to be '..\savegames_patch\Before-Black-Cove-extracted') and click the 'Extract Package' button.
After deleting the cys_blackcove.lsf file from the levelcache folder, you can start the game, load the extracted save (the game will recognize/load the uncompressed version) and the Black Cove should work properly when you enter.
Also delete any other files for areas you have not been to in this game, if applicable. The names are mostly obvious (the file for Hiberheim is theprisongardenofstoneking.lsf).