The reason for the « secrecy » is that, in the past, committees were being flooded with calls about all sorts of minor problems. For example, they were asked to refer a doctor willing to operate ingrown toenails without blood and to send 2 members to the hospital just in case an infant circumcision went wrong ... so now only an elder body is « supposed to » contact the HLC, after all avenues of treatment have been exhausted and the case has to be serious.
I personally know an elder who lives in a small town who took it upon himself to ask for a reference from an HLC member, who he knew well, in order to get a cooperative doctor in a large city hospital. His HLC friend followed the rules and told the elder to try and get local treatment first. He promised that if that was impossible, then he would see how he could help.
In my experience if there has ever been a serious case in an area (and there usually has been) everyone knows who the HLC members are (gossip and tall tales) but never worry about it much until they have a personal health problem. Then they plead with the elders to get in touch with brother X and may even try phoning themselves (I don’t blame them - they are told and believe the HLC is ahead of the times in operating procedures and can tell a doctor exactly how to perform their operation without a hitch. They also have the impression that thousands of doctors have signed up with the W.T Society, promising to operate without blood).
If you’re willing to put in the time and effort to compile a list, I believe most people on this site could give you several names. Perhaps some wouldn’t mind phoning their local hospital and asking for the names (all hospitals have, in theory, been contacted and possess documents, business cards and phone lists of members to call in case of a crisis.) The only drawback being that it would immediately indicate to everyone reading their post what part of the country they were coming from.