I'm not feeling terribly confident, since several commenters have defended it, but I'm not sure that #3 works either. I'm going to tentatively say that "since," in the meaning you want, is about the past, so only past tenses work.
Something similar to #3 is "I haven't seen her since she has started working there." To my mind, that works, since it speaks of a discrete moment in the past. It implies that her work is ongoing in the present, but the start of her work is a past moment. Of course, I don't know why anyone would say this, instead of "...since she started working there."
In short: You say "I have seen such sentences only with past simple and past perfect simple." I think there's a good reason for that. Note, this isn't so much about grammar as about ideas. Don't get the idea that "there's a rule that 'since' takes certain tenses." Rather, it's: "This meaning of 'since' is about discrete moments in the past. So it's hard to use it with verb tenses that don't handle that idea."