That's correct - AR doesn't show on DL.com. You will need to call to book.
AR is available for viewing on Expertflyer. Use EF to find the AR flights you want and then tag them on to your Delta flights. Make sure you keep an eye on your BUE connection as most AR flights to BRC depart from AEP, not EZE (where your DL flight will operate).
Yes, I'm aware of the airport transfer need. Thank you for the suggestion, I'll try that.
Side question... would a stay over in Buenos Aires for, say, a week be allowed?
For example:
1: Depart RDU
2: Arrive into EZE, transfer to AEP, fly to BRC
6: Fly back to AEP
12: Fly back to RDU