Hello unhinged,
Barry is gone this week unfortunately and he would be the exact guy to ask.
After asking around we don’t believe we have a built in function in the API that will do what you ask.
You may want to just try tribe_get_events with the title query set to the event you want. I believe all recurring instances have the same title, so they should all be returned.
If that doesn’t work let me know! I’ll follow up and see if we can get something elegant thought up.
Cheers!
– Casey Driscoll