My thoughts are that she feels your instability in "the truth" comes from those "sins". Thus, confessing them may clear up things, bring "Jehovah's Sprit" back to the both of you and then everything will be OK.
From what you have written here, I really think this is most likely. Many JWs walk around with guilt, thinking that things do not go right for them because the "broke the rules" at some peroid in time. If they just get that cleared up officially, God will then begin to bless them.
I don't really know where you can go with this. You can humor your wife, yet that will bring pain. You can try to explain to her the pointless nature discussions with Elders bring forth, but she will ignore it. You can say you don't believe in the process at all and she will cry.
However you deal with the situation, I would say that realizing her desire for "cleanliness" before God will be of the most value. You possibly may begin to push the idea that she doesn't need forgiveness from anybody but God, or something like that. Try and get her to talk about exactly what she hopes will happen. Letting her openly talk about WHY she wants to do this meeting. She may just talk herself out of it. Try not to argue and/or give your own input. Just ask tons of quesitons about what she thinks will happen and why it would be a benefit.