Did you have luck with this or did you get an external receiver?
I've got an ATA GDO11V1. Following the homelink steps, I'm able to recognise the remote (headlights flash) however the next expected step, where the tesla waits for you to enable the pairing mode, seems to be skipped. The car just says the remote has been learned and finishes the wizard, however the car doesn't open the door.
I've still got some room to keep fiddling as the learn process for these openers is a two person job, where the remote isn't portable. See how I go, would be helpful to know if you ended up having to buy something, or figured out a way eventually.