The Tonys only award Broadway shows, so The Hit List has to move to Broadway for it to be up for any awards against Bombshell or otherwise. The Drama Desk awards do Broadway and Off-Broadway. I'd imagine that this show wouldn't bother with DD and would aim for the Tonys. It seems like Derek isn't going to be happy until The Hit List is on Broadway.
In show business, no one "deserves" parts. Newbies come in and win Tonys (Hello, Sutton Foster) and longtime Broadway actors work for years and never get a break. That's just the way it goes. I know a lot of posters like Ivy, but I'm just not a fan. She's more tolerable now than she was last season, but she's still one of my least favorite characters on the show.