Well, it is called friendly-stealth-invisible, so I kinda assumed it would only worked on friendly craft. If you insist, I'll give it a try.
*Reads description of SEXP more closely*
Actually that does sound like it would work... mental note: carefully read through something before deciding anything about it.
EDIT: Yipee! That worked! Mefustae's solution did the trick, except for one tiny flaw: the ship was visible on radar for a fraction of a second before vanishing. However, I found a wa around that too: simply make the ship "Hidden from sensors". Doing this and then Mefustae's idea makes it completely invisible from the start. I don't know if you can unstealthy it afterwards, but fortunately, I don't have to worry about that, since my mission doesn't require it to go unstealthy.