First of all, it is good that this thread is any help to somebody else.
I managed to repair the unit and make it work by soldering thru hole caps. I am personally not equipped to solder SMD components (and I have yet never tried it anyway).
I replaced all of the nine 47uf 16v caps (all located on regulator circuits for the ICS), only 6 had leaking marks under it, but as I removed the three remaining, I noticed they also started leaking underneath.
I would say that it would be better to replace them with SMD caps, it will hold better on the board, but I was personally a bit in a hurry. nevertheless, I fastened some of the wonky thru hole caps with hote glue to be sure the connection would hold. The problem I encountered was that the leaking damaged the coper traces and therefore, the solder was not holding very well on the board.
Concerning the 470uf SMD caps, they were fine, the deformation is normal I guess.
Before you attempt anything, be sure to read the schematics and informations in the service manual carefully to be more familiar with the board you are going to work on.
If you need further advices, do not hesitate to PM me, I am French too, so it might be quicker.
Keep us posted on your repair!