Thank you for your reply ~kyrillix~. The problem is now solved.
I believe that I was too tired (around 2am) to envisage reinstalling everything and too sleepy to think straight.
What I've done is that I removed every files that have kreia or carth in their name from the override folder. By replacing them in packs before testing the cutscene again, I soon found that a .utc related to carth was the problem and because I only have two mods altering this character, it was easy to spot the guilty one : Admiralty.
I just correctly reinstalled the mod via its TSLpatch and problem solved. Simple, logical... excepted when you've past your bedtime.
Now, I don't know what does the file that has been replaced, or what was the origin of the problem. It is beyond my skills and as I'm just happy to have everything back in order, I won't investigate any further.
(I firstly thought a .2da file was the problem because I hate, you know, when you've got a mod that alter one of them but without a TSLpatch to help. Editing them is not difficult unless you don't know which line to modify and how.)
I should have used KMM as you say. Thanks a lot for the link, I shall make a clean install using it.