Update on this: The case has been opened without infernos or other damage to the cells (Pictures are to be added soon).
After some searching and thinking, I decided to try and open it with a scalpel. I started to cut at the front face of the battery for a little practice. After all it can't hurt to hit the print board with a blade

After a little cutting I noticed how thin an overlap was actually welded together (ultrasonic welding, for anyone who might want to know). It was also good to see which part locked in which: The top part of the casing has a rib running along the edge of the case which fits inside the lower part. So if you cut from the top part downwards, it's more likely to have plastic material between the blade and the lipo cells.
After seeing this I decided it was the time to take 'the giant leap' and open it all the way. A tense minute or two, and a small hole in the front allowed me to open it at the front by twisting a screwdriver in the hole (from parallel to the seam to perpendicular to it). From there on I could gently pull it open.
The damage seems to be a loose solder on the + side of the print board

To make access easier I also pulled the top part of the case off the cell. This took a lot more work, as it was thoroughly taped to the top with double sided tape. An old membership card did a nice job when gently forced between the cell and casing and eventually the tape gave way. During this it was critical to make sure the cells wouldn't twist, bend or anything.
In the end the loose + mount on the battery gave way, so it needs to be mounted/soldered back on. It seems like it could be an easy and cheap fix: A student electrical engineering may be able to help me to exactly figure out the problem (just to be safe) and this battery may actually be used again for training sessions and in a basher or two next season