Please do not take this in the wrong way. But the sooner you live in accord with what you believe the better person you will be. Life is too short.
See, others are telling you. Not just me. Putting aside that excellent comment, generally speaking I almost always tried to say "He/She is repentant. Private reproof. Period." So did many of the elders. Private reproof would just be inappropriate if the thing was highly known. My last JC (and I was the chairman) got out of hand because someone went over my head about private reproof and called the service desk to get them to clarify why we needed to announce reproof. The PO brought pressure on me to personally make the announcement after he heard that one of the elders had spoken to Bethel.
Is that what you are hoping for? A mess from the other two elders, a stink to get you fired? It's rare. Even had I refused to make that announcement, another elder would have. They still would not have fired me. You might serve on several JC's before your standard private reproof solution is rejected. Maybe your body is more cold-hearted than most others. If you know that, you stand a chance.
Just free yourself of the burden. If you insist on getting fired, then you have to do something that makes you look bad. Instead- Just start working on a reason to quit instead of looking bad. Depression, burdens, doubt- those are the big three. Doubt makes you look bad, but it's honest. It only looks bad to those on the BOE because you don't share it with the congregation. They only find out when the gossip starts, but by then you are fading out.