Brother: The part of your situation that I don't understand is the recomanded part of it. I don't know what would happen in the next step. For example, I am not sure if the asylum office will send final approval without second interview or whether they will call you in for another interview. In any case, divorce from the principal does not affect grant of asylum. They don't really care. The problem is you can't get greencard based on that asylum. You will need to get your own asylum approval if you divorce and you want to get greencard. In most cases, if you are coming from the same country, it won't matter that much.
It is really hard to predict. and minor mistakes can cost hugely. If you are really depressed in your marriage consult a lawyer if you can apply on your own. What you have is recomanded approval. If you apply on your own you may get a better IO and get a final approval right away. Also consider the situation in your country. In many cases, asylum interviews resulting from divorce are very easy. They don't consider the original grant of asylum. They just estublish a separate file for you. In my interview, there was no asylum questions at all. Just name and easy stuff. Also other people who went through the same process have not reported any difficulties.
The only problem I have with your case is the recomandation part. If you had final approval I would have adviced you to go ahead with divorce, but the recomadation is holding me back...good luck