Contacting your local ward or missionaries would get things moving faster. When I served my mission we didn’t have electronic referrals so I’m not sure how that works, but we did receive some referrals from Salt Lake and various other visitors’ centers. Although as missionaries we appreciated getting anything that would potentially lead us to an investigator the majority of the time the referrals were dead ends (i.e. wrong/non-existent addresses, people claiming not to have made a request for contact, etc). This served to lessen our sense of urgency in trying to contact the referral, especially when they all indicated the person was VERY interested. If your elders are busy it may simply be that your referral has been placed in the “to get to when we have time” pile. However, I would think that getting a second referral with the same info would tend to increase the feeling in the missionaries’ minds that the person was genuinely interested. If you do try to contact a local ward the best time to call would be in the evening probably Tues-Thurs. Due to the church’s lay ministry there won’t always be someone to answer the phone during the day. If you call the mission office, however, someone should be available during the day.