We've definitely experienced similar. We had success creating a form for sales people to submit when they had their own reference for a deal. We told them we didn't want to get in the way of their relationships, we just wanted to know what convos were happening so we could track it and make sure we don't burn advocates out. Since it was a pretty low lift ask, most of them were OK filling it out.
Unfortunately, we also got people on board when they started to see the negative effects of their approach. They would burn customers out and wonder why they weren't answering anymore and then come to us to ask for help. It opened the door to a good convo so they understood why we were there to support their deals.
Lastly, we have win slides with AE's talking about deals we set up references for and the impact it had on their deal. Seeing top sellers using our team helped encourage them to do so, too. We also have some key advocates within the sales teams who tell the new hires on their teams about us, how to work with us, etc. I get a lot of new AE's saying "Nory told me to reach out to you" and so it's been great to have key people pushing our message without us having to. Building those strong relationships has been key!