In those pics,I didn't see any brown jelly on your coral.Thats no to say,that yours didn't have it.If its brown and stringy mucuus then thats something completely different.Corals regulated the zooxantellae population in there tissue by expelling it out through their "mouth".
There has been no known causative pathogen yet identified that causes Brown Jelly condition.With that,the only treatment that has worked for me,is blasting the jelly off.If you have a water dental pic,that is great as the high pressure really gets it off.Then doing Lugols dips.
After reading that article,I've found the information in it to be anecdotal and some i flat out disagree with.Know wonder there was no author or references listed at the bottom of it.
Let me go see if i cant dig up another article on the subject.
edit-I found the author Albert J.THiel 1997,Now i see why alot of that info isn't accurate,its out
of date