I found but can't open eclipse.ini (bad parsing)
Well, I've gone crazy and actually searched for the eclipse.ini file. I've actually found it in: 
/Eclipse.app/Contents/Eclipse

It's amazing how much advice on the internet (including eclipse.org!) points to: 
/Eclipse.app/Contents/MacOS

It must have been true at some point but perhaps with newer versions, this is not necessarily true anymore, which is why I would like to keep this question and this answer despite the basic mistake - in order to inform other people with the same problem.