When I run into a possible match with an unlisted profile, unless I have really good reason to believe it might be the person I am interested in, I simply ignore it. Just mark it as a rejected match and move on. Especially if the name is a relatively common one.
If you have serious concerns that this might be a match to one of your family tree, then you can file an Unresponsive Profile Manager Request Form, as I believe you said you have done before.
But if you have a very large gedcom you are processing, it doesn't make sense to check out every Unlisted match.