I managed to get a trip into Vallgornera in 2011 - I believe we contacted the Federacion Balear Espeleologia (http://www.federaciobalearespeleologia.org/) on the email address federaciobalear@yahoo.es. Probably best to write the email in Spanish/Catalan as they didn't speak much English. We had a great trip, it is an amazing place!
This Easter a few friends of mine from MUSC has another trip in there - I believe they contacted someone through speleo.club.mallorca@gmail.com and they have a basic website here: https://sites.google.com/site/speleoclubmallorca/about-me. I believe they had to pay for access and again they didn't speak much English so again Spanish/Catalan is probably best.