I think this has potential, but it's just the naming of it. As in the case of Where's My Mummy?, there was already a mystery going that they didn't start, they only found it. What the gang did (minus Velma) wasn't a mystery whatsoever.
In fact, it is included into the category due to the involvement of Velma. This category includes stories in which at least one gang member was involved in the mystery (that's why it's called "Mysteries staged by members of Mystery Inc.", not just "Mysteries staged by Mystery Inc.").
Maybe that's a better alternative. I just feel maybe it should be nailed down to the complete involvment, like "Cases with members of Mystery Inc. as the monster". That might be a bit too long, though.
This variant is too narrow because some of these stories, like Clueless, don't have a "monster" at all, and in others (like Chupacabra-Cadabra) the "monster" was some random person, but he was in cahoots with Mystery Inc. members.