I don't know what your tech stack looks like, but it seems relatively trivial to build. Back in the day I built a tool for viral email lists which tracked referrals like you described.

If you consider it a long-term, integral part of your service and you can use the flexibility it's worth building it yourself. Integrating an existing service might end up costing the same number of development hours.

If however you want to provide a marketing person with the flexibility to tweak the goals (and potential rewards?) then an off-the-shelf solution might be more useful. I remember a solution in addition to the one's you already mentioned, but can't recall its name right now. Will do a little digging and follow up if I find it.

Edit: here's a service you could use: www.getambassador.com