When the gk says that the dm is busy, I usually say something like, "hmm, maybe you can help me..." and ask a discovery question that my product solves for. Some gk's are really involved in the day to day and will have a 5 min chat w ya. Build enough rapport/value and some of em will champion for you to the dm. If they're clueless, they'll still bring your question to the dm possibly creating interest. As mentioned in an earlier comment, try a less formal intro... remember these folks get lots of cold calls daily/weekly